I get that humans can't understand the talking animals, but do they not notice that they wear clothes?
They probably do, but in this universe there doesn't seem to be anything unusual about animals wearing clothes. The humans would just think of it as normal; maybe they'd notice it more if they saw an animal that didn't wear clothes. "Hey, look at that mouse, Bill, not a stitch of clothing on him! Times must be hard."
Why is Tanya so arrogant in the last two films? In the first ones she was more close and lovely to Fievel.
She's growing older and entering the age where she begins thinking of herself as "grown-up" and "done with childish things." And so the younger Fievel, who is still playing around, comes across much more as an Annoying Younger Sibling in her eyes, hence she has less patience with him. It's not an uncommon phase for older siblings to go through.
An American Tail
Where did they get the idea that there were no cats in America in the first place?
Same way the human immigrants got their unfortunately false misconceptions about America.
Yup. "The streets are paved with cheese" was a reference to an actual belief that America was so ridiculously rich that they paved the streets with gold.
Why did all the other sweatshop workers never think of tying their sheets together into a rope and going out the window before? Why did they need a little kid to tell them they could do that, when at least one of them is clearly an adult? And what made them think Fievel was crazy and it wouldn't work?
How high they were up was probably a discouragement, and Fievel's idea was crazy. Crazy enough to work.
More likely, they just didn't see the point. To even be "working" in the sweatshop they must have no family, no money, no place to go. Why run away and risk ending up on the streets starving, when they could stay where there's garanteed food and shelter?
When the cats capture Fievel, why do they put him in a cage instead of just killing him?
Maybe they were planning on sending him back to the sweat shop?
Warren could have been planning to use Fievel as some kind of bargaining chip, perhaps.
Fievel Goes West
Why didn't Fievel follow the train tracks after going overboard?
Because he's a little kid and doesn't think things through very well.
How do the Native American mice have all that food in the middle of a desert?
There are numerous animals and vegetation that are capable of surviving in the desert, and there are trade routes between those who live out in the desert and those who live closer to oases.
On a somewhat related note, in The Treasure of Manhattan Island how in the heck are the Native Americans growing crops in an underground cave where there's no sunlight? Where do they get the huge fruits and vegetables we see them feeding Tiger?
How did NONE of the mice realize they were building an enormous, fully functional, and completely undisguised mouse trap?
Maybe they all just never pay attention?
Same reason Cat R. Waul has no trouble tricking them again in quite a few episodes of Fievel's American Tails.
Cat R. Waul was planning to spare Tanya because she's his "diva." Did it ever cross his mind that she might not be that enthusiastic about performing after witnessing him murder her entire family?
Something that's always annoyed me: Fievel's dad in the second film telling him to effectively forget about Tiger because "he's still a cat." But then when they get to Green River, he instantly just accepts cats can be good too? Why?
They weren't under the impression that the cats in Green River were good until after they got there, right?
The villain used a puppet to pitch the idea of cats and mice in Green River getting along. Admittedly the father's line there (now that I really think about it) comes later on in the film. But that doesn't quite explain why they weren't too bothered about uprooting for a promised land, again.
Again, Truth in Television: Plenty of immigrants actually did head west because, again, they were told there was opportunity there. It was actually a bit closer to truthful, since even if they would still face social stigmas for being Irish/Jewish/Polish/whatnot, there was a semi-decent chance to make enough money or be invaluable enough that the social stigma didn't matter.