Translation:I don't like doing homework.
Iya has more of a sense of revulsion to it than this translation conveys. For want of a better word it's closer to yucky than don't like. But even yucky isn't the right word. Something that even the thought of doing evokes an immediate and strong feeling of repulsion in you, something that your whole body rejects, a strong sense of not just not liking something but also not wanting to do it. There's not really a suitable equivalent to iya or yada in English. Yucky, icky or gross make it sound trivial and childish in English. Perhaps a strong aversion to? People generally don't speak like that though. You don't hear people saying "I have a strong aversion to...."
A good way to think out it is as a no with a grimace. So unless it's something or some situation where you'd physically grimace whilst saying no, いや is not the word you want.
Of course this also include joking いやs with friends, where you'd probably smile or laugh whilst saying so but still be grimacing a little. e.g. whilst shopping friend A picks out a really ugly shirt out for you as a joke, you exclaim なにそれ？いやよ！with a grimaced smile. You both laugh, the end.
The exaggerated/direct nature means gives it the childish feel, so definitely not something you'd say in a polite situation.
I've only received a couple of emails saying my suggestions were accepted, but I've noticed that since I first went through the course that other things I have suggested have been changed, so I think only the first person who makes the suggestion gets an actual email.
It seems like they go through one module at a time, because I still sometimes hit a review module where everything is a mess, whereas other modules I'll be pleasantly surprised that all my answers are being accepted.
Essentially they are the same although する is probably more commonly used. Also やる is arguably used for specific things - sports, playing an instrument, certain constructions eg. やってみる - try and see (literally do and see). Also one key difference is that やる is an ichidan verb and conjugates accordingly while する is one of only two irregular Japanese verbs - the other being 来る. Just a wee update - する is also commonly used for compound verbs ie. noun + する--> compound verb eg. 勉強する - to study, 料理する - to cook, 県ぶする - to sightsee/go sightseeing. I've also only ever encountered the following polite construction with する - 話します-->お +話し+します-->お話します (it still means to talk but just a more polite way of saying it).