There's a lot going on in this question, so I will try to answer each part separately.
First off, "I hate to do that" is not grammatical, or, at the very least, it is very old fashioned and sounds wrong to a modern speaker. It is better to say "I hate doing that". You can say both "I like to do that" and "I like doing that", but "hate" doesn't work exactly the same as "like".
That said, "I hate doing that" means "Every time I do that, I hate it". For example, "I hate eating peas". It is used for things you have done, and know that you hate.
"I would hate to do that" is grammatically correct, and it means "If I were to do that (in the future), I would hate it". It is often used for things you haven't done, but know that you would hate them. For example "I would hate to run a marathon." I have never run a marathon, but I still know that I would hate it. I cannot say "I hate running marathons" because I don't truly know that I hate running them if I have never tried.
You also mention "I would like it" meaning "I want it in this particular occasion." That is true, but it's a specific usage of "would" that is used for politeness. "I would like to leave" is more polite than "I want to leave."
"I would like it" has another meaning as well. If I said "I think I would like skydiving" that does not necessarily mean I want to go skydiving right now, but in the future if I went skydiving, I think I would like it.