For starters: Why did the kids show themselves in daylight just before the helicopter attack that killed two of them? By that time, they should have had it very clear that "showing oneself by daylight" equals "death."
Truth in television. Insurgents in real life show themselves in daylight a lot, too. Often with similar results.
Also they had learned a lot... to the point that living the way they needed to was becoming physically and emotionally exhausting. They basically reached the top of the competence curve and started rolling down it. This applies to the following question too... it's not that they don't know better, it's just that they've become too burned-out to listen to their own better judgment.
Not to mention: Why weren't they a lot more suspicious about a bunch of food that just happens to fall off a truck right near where they're watching?
Both questions are answered by the fact that they were damn near starving. They'd already run through the last food they had and were probably hesitant to do too much hunting for fear of alerting Soviets to their position, if there was indeed much of anything left for them to hunt. It was nearing the end of winter and by then their desperation simply won out.
Doesn't explain why they didn't send one person to check out the box, instead of exposing their entire group to ambush.
Because 1) that means the leader either has to pick someone to go or has to go himself and make everyone wait, which at that point would have bred resentment, and 2) it wouldn't have mattered, the ambush didn't consist of a couple of guys waiting to jump out and go "A-ha!"
they did have one person check it out before they all ran down to gather up the food then they retreated to a semi covered area and it even appeared that some time, probably only 30 min but still, before the helicopters showed up. still not terribly bright on the kids part but it was apparently a well thought out ambush buy the Russians to get them to let their guard fully down, which worked shown in how one of the girls was playing around with the food
Why did they execute Daryl? It was obvious he didn't betray The Wolverines willingly, and no one (on their side) got killed. If the tracking device was really a problem, couldn't they just send him on his way until he either crapped it out or got ambushed so he could possibly take down a few more soldiers with him? For that matter, why did Daryl go back to the Wolverines if he knew about the device? Couldn't he just deliberately wander aimlessly to keep them from finding the Wolverines while trying to leave some sort of coded message warning about his predicament?
Given that the Wolverines make it to and from town on foot, that puts a rough upper limit on how far away their base is. The Spetsnaz almost certainly told him 'you have X hours to make it back; try to stall any longer than that and we'll pop your family just for fucking around with us'. After all, stalling for time would be the obvious move. As far as leaving a message, the kids are not professionals — they don't have dead drops and contingency plans set up, and its not like he can use a radio or call them on the phone either. The only way he has to get a message back to their camp is to have someone carry it there on foot, which is obviously not an option.
So why doesn't Daryl at least tell them "Hey, they made me eat a tracker" when he gets back so at least they'd be prepared? And if they made him swallow it, wouldn't he have just crapped it out soon enough? Also, the idea of using his family as leverage doesn't seem like it would be useful at that point considering that until then the response to a wolverine attack was "Murder a bunch of random civilians", despite the fact it wasn't actually stopping the attacks and was just pissing the wolverines off even more. Considering all the war crimes we see early in the movie, it's really hard to see why any promises not to murder ones family if one cooperates would be honored.
Because if the Wolverines are running away and/or lying in ambush when the Russians get there then it is obvious that Daryl warned them, at which point they kill his family and kill him. And remember, Daryl has already decided to believe the Russians' promise not to kill him or his family if he does what they want (whether or not this belief would be justified is another thing entirely, but he's decided to buy in so his decisions will be informed on that basis), or else he'd never have gone back to the camp at all but just told the Russians to kill him right then and there.
To answer the original question - the reasons the Wolverines execute Daryl is both emotional and pragmatic. Emotional: after all they've already lost, they're that pissed off that someone violated what little scrap of safety they had left. Pragmatic: their choices are either 'take Daryl with us', 'kill Daryl', or 'let him go'. The first choice is an obvious non-starter, and the last choice leaves an information source alive for the Russians that is very familiar with them and how they think, and knows as much about the local terrain (that is, where they're likely to try and hide next) as they do. So by Hobson's Choice its door #2, feed Daryl a bullet.
Why don't the wolverines get more recruits or at least assistance from the townspeople as time goes on? Considering how half the town is either in concentration camps or randomly executed every time the wolverines strike, one would think after a while the townspeople would really, really want to help drive their oppressors off. I would think that the heavy-handed punishment of people not involved by the communists because of the Wolverines blew up a tank would drive at least some people to figure "If I'm gonna get shot, I want to take at least one of them with me".
Jed is shown refusing to take any more recruits at one point, having his hands full already. The Wolverines are shown as ultimately unable to feed themselves, and also as slowly running out of weapons and ammo - having more recruits available would be useless, because they wouldn't have anything to eat or to fight with.
What exactly makes this remote small town so strategically important that it should be taken over in the first wave of the invasion, and then maintain a heavy military presence there at all times?
The rail yard, and the part where the front lines are only a couple dozen miles away. The town is a supply depot and logistics nexus for the heavy troop formations up on the line; that explains both the heavy military presence (its a supply and service depot), and the part where the troops stationed there are not the sharpest combat troops but instead are auxiliaries from satellite nations like Cuba and Mexico (the first-line combat formations are on the line, places like this are where you put the sort of second-echelon grunts you use to move boxes, guard ammo dumps, and keep the roads open.) It also explains the Spetsnaz being sent in at the end; random partisan guerrilla attacks off in west bumfuck aren't important, random partisan guerrilla attacks that are actually starting to interfere with your logistics train are something that needs stepping on hard.
So I get the Silos somehow got taken out by a first strike(despite things such as the fact Silos are damn hard to kill even if you are dropping another nuke on them). So what happened to the rest of the Nuclear Triad? The US Navy had quite a few Submarines(which presumably are extremely hard to track, even by the rest of the US Navy. You aren't gonna find them until the missiles are already in the air) whose sole purpose in life is to wait for the Go code to come down and launch their 16 or so nukes(plus more if the missles were MIRV'd) at the USSR, and the US Air Force is famous for Strategic Air Command keeping nuclear armed bombers in the air 24 hours a day just in case of a Soviet Attack. Being as the beginning of the film established the Soviets were being incredibly aggressive and Europe pretty much decided "Screw NATO" you'd think all of those Nuclear Forces would be on High Alert at all times(so that taking them unawares would be extremely difficult if not impossible). And it's really difficult to argue we just didn't use the nukes, because if you aren't going to us them when the enemy (presumably) already struck first AND invaded your country, when would you use them?
Maybe whoever was in charge decided that it was better Red than Dead. That was always the big unknown in the Cold War, would the US President really do it. Would they decided to irradiate the world and doom humanity to living in the dark ages (at best), or would they treat the nuclear arsenal as a big bluff and once it had been called; decide that it was better lose and have some vestiges of their nation (not to mention every other nation on Earth) survive and maybe rise again. Its never really been answered, thank God, and you can certainly argue some Presidents would be more likely to go one way and some the other, but we'll never really know now. So maybe in this, the President at the time was one that decided that it was better to be conquered and use mostly conventional weapons to resist. If you think that sounds far-fetched; when they first developed Atomic Weapons in the Manhattan project and were working out the maths on whether they would ignite the atmosphere, it was decided that if the chance of atmosphere ignition were higher than three in one million it was better to let the Nazis and Japanese win (even if it meant occupation of the continental United States), in order that human life would continue and freedom one day be won again.
You forget that the President isn't the only one involved in this decision. If the Russians nuked the midwest, took out NORAD(presumably) and invaded the midwest in an suprise first strike, if the President decided that even a soviet first strike and executing American civilians in occupied areas and putting Americans in gulags wasn't enough to warrent nuclear reliation, I can imagine congress, not to mention to Joint Chiefs and the Do D, would be looking for anyway to remove the President from office and put someone into office who would strike back. Though just allowing the Russians to invade the US mainland and Nuke us would likely be more the enough for the president's approval rating to drop to 0% pretty damn quickly. Refusing to strike back would be asking for a military coup.
For that matter, it's outright stated that the Russians nuked the Chinese. China has it's own nuclear arsenal. So again, why isn't half the USSR glowing in the dark?
Maybe it is. There are still Soviet troops in the US.
So, WTF was going on during the tank battle? Two Russian tanks and one US tank just show up and start slugging it out in the snow, all three completely unsupported by any other tanks, infantry or support vehicles, which seems really odd since it runs contrary to basic armored doctrine(Tanks support infantry, Infantry support tanks). Most importantly, Infantry keeps enemy infantry from getting close to tanks and...say, climbing on top of the tank, prying open the hatch and dropping a grenade inside(killing the crew). Which being said, why do the wolverines completely fail at something that should be so simple? Both Russian tanks seem to be buttoned up, so they wouldn't be able to see the wolverines anyway(unless the wolverines stood right in front of them).It should have been a simple matter to climb the closest one, kill the crew, and use the disabled tank as cover to assault the other. There's a single machine-gunner on the other tank who poses the only threat to this plan, which should be no problem for them considering how easily the wolverines seem to wipe out entire squads and convoys. What makes it worse is that they have a senior military officer helping them(who dies in the assault) who doesn't seem to understand the whole "Sneak up on tank, use tank for cover against other tank, kill tank crew, repeat" idea.
There is an understandable reluctance to go anywhere near the Russian tanks that are in the process of being shot at by American tanks, especially after the Colonel dies from friendly fire while doing precisely that.