In Starcraft 1, the zerg were chasing ghosts/Kerrigan for a psionic to infest. Why would psi emitters attract zerg now?
That wasn't the only reason even in the base game. Back in Brood War, they could still use psi emitters to attract feral Zerg (that's how Kerrigan got some of them back under her control in an earlier mission of the Zerg campaign). Maybe Zerg just feel naturally attracted to the closest psi emissions when no Hive Mind to control them is available?
The original manual states the zerg are naturally sensitive to psychic energy in general. As most zerg lack the intelligence to recognise they're being manipulated they simply respond to the strongest psionic call around. Once they're there they act as zerg always do and attack everything around them.
Secrets are what made them suspicious?
During the flashback sequences in mission 6: Flashpoint, Nova and Stone make a comment that they haven't been told about the devices they're setting up. And this is what makes them suspicious. But unless "Operational Security" just doesn't exist in the Dominion Ghost Corps, this shouldn't be suspicious in the slightest. Covert operatives - hell, soldiers down the chain of command in every branch of every military that has ever existed - are only given information on a need to know basis. Not being told all the details about a mission should not be suspicious in the slightest for a veteran Ghost operative like Nova; that's be par for the course. There were plenty of other dodgy details about that mission that should've tipped them off the Defenders of Man weren't on the level.
It might have to do specifically with what the devices are supposed to be for, and what their mission is supposed to be. Experimental weaponry against zerg and protoss has been used routinely before, so not even telling other parts of the military (who would presumably want to know about such weapons and can keep the secrets well), could seem strange in this circumstance.
It wasn't the secrecy surrounding the devices that first made them suspicious; they had only recently been developed, and Stone even says that not being informed about their development could have been an oversight. However, Nova pointed out at the start of the conversation that the Zerg were supposed to no longer be a threat, and yet they were suddenly being handed brand-spanking-new zerg-incapacitating tech and ordered to set it up in the middle of a heavily populated city while making sure absolutely nobody noticed what they were up to. They probably realized that if the Dominion knew there was an impending zerg attack on the planet they could have simply parked a fleet in orbit, or started prepping the civilians for evacuation - at the very least there would have been no need to hide the fact that they were setting up anti-zerg devices if there really was a threat to the planet.
Logic in the Defenders of Man attacking the Tal'darim
I know that the DOM intend to destroy the protoss once they've taken over the Dominion but even they should know how advanced they are and the fact that the Tal'darim in particular are vindictive and will stop at nothing for revenge.
Perhaps the goal is to get the Tal'darim to attack the terrans in general, the mothership might well have destroyed the stadium if Nova hadn't interfered. It also might be possible that the Defenders want the Tal'darim to attack them, than fend off the attacks in the same way they do to the zerg, and the Tal'darim being more powerful than expected is a miscalculation on the defender's part, or the terrans have gotten more confident about fighting protoss in general after years of warfare.
Alternatively, it could be the intel the DoM have on the Tal'darim only concern Nyon's faction (the ones encountered by Raynor's Raiders in Wings of Liberty) and the DoM are thus under the impression that all the Tal'darim are a bunch of Axe-Crazy zealots that can be manipulated into attacking Terran colonies much like the Zerg, instead of the very competent Badass Army led by a Magnificent Bastard like Alarak, making this less Bullying a Dragon and more Mugging the Monster.
Going AWOL after killing General Davis.
Why would either Nova or Reigel decide it's better to go AWOL than simply report back to the Dominion? Yes, there's some comment about their current lifestyles being all they've ever known but they can continue those under Valerian. Reigel wants to keep developing weapons and technology but there's nothing stopping him from doing that on the Dominion's payroll. Nova remarks about how there'll always be enemies of the Dominion that need to be taken out, but she's the Dominion's top Black Ops agent. That's already what she does for a living!
Two words: Plausible Deniability. With her as a free agent, Valerian can deny that the Dominion has anything to do with her. As Valerian wants to run a PR program with more substance than his father's, he cannot be seen to be relying too much on black ops.
Not to mention, it adds a Terran side of conflict to the story for a future DLC. As Alarak refused to join the united Protoss at the end of the Epilogue, it left a Protoss faction to fight against in Covert Ops. If Blizzard decides to do a side-story on the Zerg or Protoss later, they can bring in Nova's team (or the Defenders of Man) as antagonists for the Terran side.
What happened to the Tal'darim?
So, where did Alarak and his people go after Dark Skies? They say that the Tal'darim have taken high casualties, but anyone who's used him in Co-op should know what Alarak thinks of that and I severely doubt that he'd just pack up and go home. I guess maybe Valerian was able to get him to stand down by informing him of Davis' death, it just seems strange that there wasn't even a note about another round of negotiations to get Alarak to stop glassing Dominion worlds or something similar.
If nothing else, Artanis likely interceded on Valerian's behalf and told Alarak to knock it off. Alarak may be bloodthirsty, but he's also smart enough to not pick a fight with both the Dominion and the Daelaam Protoss at the same time.
Since the Tal'darim are a Blood Knight faction that places utmost importance in Asskicking Equals Authority, they may have gained some respect for the Dominion after being repelled. Alarak already showed in Legacy of the Void that he starts respecting, at least begrudgingly, those that prove they can kick ass and take names, such as Artanis.
The strategy of the Tal'darim during Paradise Lost
Why would the Tal'darim bother charging up their Mothership to kill the Defenders' base? Why not just send their forces after them like they did against the Dominion?
Or better yet, why not simply destroy the Defenders from orbit like with the zerg? They had no qualms about doing so in the cutscene prior to Dark Skies.