I feel like you guys are misinterpreting a lot of the information in the series. True, the Yeerks are always described as a plague on the galaxy or whatever, and in HBC Esplin specifically says that the Andalites are the dominant race in this arm of the galaxy- but look at that realistically. "This arm of the galaxy" contains tens of billions of stars (Joe Bob Fenestre couldn't buy all the stars in this galaxy for a quarter each), and even if you say only 1/10 of 1% of them has a potentially inhabitable planet, that's still tens of millions. I guess what I'm getting at is that the races of the Animorphs universe obviously have a major tendency to exaggerate... unless Esplin was speaking about the Andalites' technological dominance.
Anyway, the Yeerk Empire had obviously not spread to a million star systems, and they could not possibly have been raging across the entire galaxy, so why assume they were on any more planets than we heard about? Maybe a dozen planets/moons in my guestimation. It always seemed to me that the reason we only saw Taxxons and Hork-Bajir used as hosts in the main series was that they were the most readily available to the empire- other conquered planets seem to have yielded very low numbers of hosts. It always seems that humans vastly outnumber any other species in the Aniverse. 6 billion hosts would make the Yeerks unstoppable, even to the Andalites, and they know it. I got the impression while the Yeerks were scouting other planets and attempting to enslave the populations there, but that Earth was far and away the ultimate Yeerk prize. The majority of the Yeerk force would almost definitely have been concentrated here. By defeating the Yeerk force on Earth, humanity managed to essentially snap the backbone of the empire, and within 2 years you wouldn't have much to do besides hunt down renegade Yeerks. What baffles me is why the Andalites took so long in getting here; probably didn't see us as advanced enough to pose any sort of threat, but in my mind that makes the Andalites arrogant to the point of idiocy. Which actually fits their actions throughout the series, so...
Yeah, I know; there were 47 Vissers, so why weren't there more here? My thought process is: who's to say there weren't? Visser 3 obviously needed officers, so why can't 10 or 30 of them have been Vissers? Just because we didn't hear about them doesn't mean they weren't here. Visser 3 was just the highest ranking Yeerk on the planet, and the one assigned to head the invasion (and my guess is that Visser 1 was used for her strength in starting invasions, and Visser 2 was a douchebag who sat on the couch on the Taxxon planet watching Survivor reruns or something).
I never got the impression that the Andalites were a very imperialistic race- they seemed pretty content to stay on their own planet and explore the galaxy. Heck, judging by the fact that, before the war, they were only allowed to have one child per family (according to Elfangor in TAC) their population would actually have been decreasing (and Seerow got to have 2 kids because he was a high ranking prince? Who knows...) The Yeerks, on the other hand, spend every waking minute trying to figure out better ways to increase their hosted population, and have fully enslaved two races with populations large enough to be worth mentioning. Truthfully, you could skew the Yeerk population increase however you wanted by tweaking the percentage of Yeerks that breed, the frequency with which they do so, and especially the number of grubs that are produced in any Yeerk mating... incident. If forced to guess, I'd say they probably breed to fit the environment. In the full pools of the homeworld, Yeerks wouldn't breed often, but with plenty of space in artificial pools and plenty of hosts for the Yeerks to take, they breed far more frequently ("So you have to choose between life without sex and a hideous, gruesome death? Man, tough call"). In any case, my point is that I see no reason the incredibly ambitious, expansionist Yeerk empire couldn't become too much for the Andalites to handle within a few years. The only thing holding them back would be a lack of hosts. Which, conveniently, Earth remedies nicely.
As for their quick technological advancement- that makes sense too. You have 250,000 Yeerks just sitting in a pool with nothing to do but study Andalite technology based on the computers. Even a fraction of that number could make significant advances. On top of that, the Yeerks have an advantage that puts them light-years ahead of human beings when it comes to learning- they can take hosts. By the time the Yeerks were building ships on the Hork-Bajir homeworld, they had the technological knowledge of the Andalites and the Ongachic at their disposal, and maybe the Skrit Na as well if, as Terenia said, they infested a couple of them. They had the technology of all three races to reverse engineer and to assist them in construction (at the very least, construction of construction equipment).
And yeah, the Hork-Bajir know to fear danger, but nothing in their experience would suggest to them that the Yeerks would be dangerous. They take a Hork-Bajir, lead him away, and soon he's back, seemingly unharmed. There's absolutely no reason to fear them- a peaceful infestation out in the open seems not only plausible, but it appears to me to be the best way to go about capturing Hork-Bajir hosts.
Give our Lady Applegate some credit, guys. She might not have the memory for details that RAF has collectively, but she's still a pretty consistent sci-fi nerd. I don't see any inconsistencies in the way the war worked out.