The Jews had to ally themselves with the Lizards since the Nazis (and several other ethnic groups) want them dead. Flash forward to Homeward Bound where it is implied that the now technologically outdated Lizards will shortly lose their influence due to the tech gap. Then recall that Nazi Germany still exists, Britain was last seen becoming a mirror of Nazi Germany, and a lot of humanity views Jews as traitors to the human race. This cannot end well.
Best case scenario: the Jews emigrate to Lizard territory on Earth (incidentally, Palestine is controlled by the Lizards) and become complete Quislings. The United States and Canada are still relatively sympathetic to those Jews who don't choose that route, and Japan is more or less indifferent (and may welcome potentially loyal colonists in their territory). Alternatively, both the humans and the Lizards have interstellar colonization capability at the end of the series, so the Jews might emigrate to another planet entirely (the Soviets are also developing their own starships, and have used this strategy before to deal with troublesome Jewish populations).
In Homeward Bound, The Doctor AKA Henry Kissinger, although he's never called that fails to revive properly from cold sleep, and Dr. Blanchard says that he may well have died en route, describing it as "dying in slow motion", an idea which makes Glen Johnson shudder.
The Race believes (based on previous conquests of the Rabotev and the Haliss) that all life in the universe is at least somewhat based on reptilian physiology. Thus, they are shocked when they discover our world full of mammals, and wonder what happened. However, if the dinosaurs had not gone extinct, and remained the dominant life-form of Earth, it's entirely possible that they would have evolved into something self-aware, like us.
That may be, but the surface of the Earth would still be mostly covered in water. The Race would likely still have to deal with multiple empires and/or not-empires.
The Race has space travel, advanced computers, holographic projectors etc., but their weaponry is similar to late 20th century American equipment (incidentally, the time and place of the novels' writing) and no better.
They probably unified their own species before any faction developed better technology for internal warfare, and didn't have to improve in order to conquer other aliens they encountered - which were much less advanced than themselves. Indeed, the very thought of needing to adapt to an opponent was alien to their sense of superiority when the plot started.
How did the Lizards ever evolve into a technologically advanced society at all?
The natural instinct of the hatchlings is to avoid adults, and the natural instinct of adults is not to give a shit. Seems like this would lead them to develop a very individualistic lifestyle, like tigers or great white sharks. The very casual approach to sex toward which their physiology predisposes them makes it even more likely. Only animals whose instincts are to socialize extensively would be likely to form complex societies.
We only know from the novels that this is how they view themselves and their history at present. They could have been a more "familial" species before being conditioned to direct their attachments to society and its leaders over the millennia. To support this claim, when one of them is presented with a human baby to look after, he does bond to it after overcoming his ingrained reservations, and personal relations matter a lot to some of them. Alternatively, the "loyalty to the group" trait may have been there from the very the earliest stages of their development as a species: picture a pack of wolves or a pride of lions whose only loyalty is to the alpha male, and may be all descended from him. Scary.
Then you have the slow rate of technological development—which should be no rate of technological development. Someone said, somewhere along the way, that it's unnatural to have scientific advancement reach a level that's noticeable within a lifetime. Now since new hatchlings are hatched, and elderly Lizards die, every year, it's always within someone's lifetime. So even if every invention and discovery gets sealed in an envelope by the inventor or discoverer with "Do not open until my death," their next of kith—they don't have next of kin, of course—is liable to say "This has to be a blueprint for something that didn't exist when I was hatched so I'm going to ignore it." So they should remain at whatever constitutes Level One of scientific and technological achievement ad infinitum.
You're taking things too literally. What that actually means is that in forty or eighty years you go from a biplane to a slightly better biplane. You don't make the jump from biplanes to jets and then to spaceships within the same century.
The Race are implied to be perfectionists. They will improve their current technology until it's 99% safe and efficient before even considering something new.
Why would a race that has never had to build warships have a word for "cruiser"? "Landcruiser" implies there are other kinds of cruisers. By the same token, they have no business refering to their spacecraft as "ships", as not having an Age of Sail means they'd never assume that Space Is an Ocean. While it would be acceptable to assume it's just the closest translation of the term, there's the part where Liu Han hears them call their planes-that-never-come-down "ships" and doesn't understand why.
IIRC Much of the Race's homeworld is desert, so it's possible that in their culture and lexicography the desert took on the same significance and meaning that the ocean has for the inhabitants of Earth, and that many of the same terms (or alien equivalents of the same terms at least) we use to describe concepts relating to the ocean were in the Race's culture applied to the desert instead.
If lizard tech is so advanced, why do their landcruiser commanders still need to stick their snouts out of the turret to see what's going on? They have pretty advanced cameras and computers, as well as holo-projectors. They could very easily set up cameras in a 360-degree arc, kinda like modern M1 Abrams tanks.
And commanders in modern Abrams tanks still stick out their heads when they are able because unless most of the tank is covered in cameras, even a 360-degree array still has blind spots.
In the Second Contact, the Race obliterate Germany when they break the ceasefire. Yet despite the repeated warnings that they will react similarly if they ever discover who blew up one of their colony ships (the USA), they retaliate by... dropping a single nuke on Indianapolis. Aside from Creator Provincialism, this is dumb strategically too - the USA was the biggest threat to the Race too!
The Race had been seriously weakened in the process of obliterating Germany and was still recovering when they found out: trying it would have weakened the Race on Earth to the point that the Soviets would have easily walked over them (the Soviets actually make the threat, stating that the USSR would not abide an attack on one of the two remaining major human powers and would launch a counterstrike on the Lizards in the event they tried to attack the United States). Thus Atvar tried a Batman Gambit: first he threatened to obliterate the US, and when they tried to negotiate he let them choose between having a city obliterated or giving up the technology for attempting such an attack again (nuclear weapons and missiles, including the ones used in space travel) expecting they'd choose to give up that pesky technology that allowed the US to fight back in case the Race tried another conquest. Thus when President Warren told him to nuke a city but to please warn him with a minute to spare he had been caught by surprise, but had to act on it.
That may well be accurate, but it just shows that the Race are dumb (or that their supposedly impeccable planning is a big lie). They threaten to sterilize the Earth - but don't have the capacity to do it? It's even worse when you realise that the world's largest Uranium reserves are in Australia - which the Race holds!
It's more a question of Atvar's will to actually go through it and human ability to thwart him. About the will: the Colonists convinced Atvar to not sterilize Earth even before he started the invasion, twenty years before they were bound to arrive, and once they were actually there Atvar will need a good reason to actually sterilize Earth (also because trying to evacuate them on the ships would be interpreted as preparation for Armageddon, and the humans would strike first). Then there's the fact that since the invasion Earth forces have developed anti-missile capabilities, and he has no idea if enough missiles will get through.
Plus a large portion of the Race's nuclear weapons were destroyed in the first book by the German's railway gun.
He had twenty years and the uranium depots of Australia, Africa and South America to rebuild them, and the need to do so.
It is pretty much stated that the Race's invasion fleet does not carry anything that would allow them to produce anything. They actually have to convert human factories to get ammunition for their weapons, and they are inferior since the machine-tools required to produce anything at Home level are coming with the Colonists. Besides, the Race thought they would be fighting against medieval forces at best: they would have believed that the nukes they brought with them would be more than enough, or that they would not even have to use them at all. Why would they bring the complex machinery required to make more?
In Homeward Bound, a Lizard cleaning crew accidentally frees some rats humans were using as taste-testers. They escape into the sewers of Home to reproduce and wreak havoc. Turnabout is fair play, but why hasn't Atvar insisted from the beginning that they only bring down males or only bring down females? Why were they allowed to bring a breeding population down from their ship in the first place?
The Race has a hard time distinguishing between human males and females; why would it be any easier for them to spot a breeding pair of rats? And the humans need a steady supply of rats, as some of them may not survive their assigned duty for whatever reason. Easier just to breed your own rats rather than keep calling the ship for new ones.
The rats are also a backup food source.
This one bugs me: Why would The Race, which has no concept of family lineage and especially no concept of legal fatherhood, develop a hereditary monarchy? Wouldn't it be more logical for the Emperor to choose his heir rather than to father one through the convoluted "find a group of select females for the Emperor to mate with and sequester those eggs" process? It may be tradition now, but why would the Race start to care about who's the Emperor's son when they don't care at all about paternity in any other context?
Because they believe in the divine right to rule and understand inheritable traits (or possibly the other way around). When the current emperor dies, he joins the previous emperors in shepherding the souls of every citizen of the Empire, and this duty/capacity/birthright is passed down to his hatchlings. Or so The Race believes.
Because the hereditary monarchy existed before they altered society to make them loyal only to the Emperor.
to deal with troublesome Jewish populations).