Let's look at this:
I've already contacted him for that book, he emailed me he has still copies left ...But since then nothing, although I have sent many emails he did not answer.
Focusing on your two specific questions, "he emailed me" is perfectly correct. It's in the past and you've used the correct tense here.
For the second one "he did not answer". I recommend using the present perfect here:
"he has not answered"
It is still possible that he may answer in the future, so all you can say is that, up to this point, he has not responded (you may also want to use "responded" instead of "answered").
So, now we've got:
I've already contacted him for that book. He emailed me he has still copies left, but since then nothing. Although I have sent many emails, he has not answered.
A couple of slight edits might make this a bit more natural:
- consider "about" instead of "for"
It's completely possible you actually mean "to ask for a copy of that book" (which is what "for" implies) but, particularly if you don't want to imply this, "about" may be a better option.
consider adding "saying/stating that" to the first sentence to be more clear.
using "and" instead of a comma will help the flow of your first sentence, connecting the two parts as cause and effect.
I've already contacted him about that book and he emailed me [saying that] he still has copies left.
- Consider reiterating what you mean by "nothing" by adding "I've heard"
But since then, I've heard nothing,
- Consider adding "him" for clarity
although I have sent him many emails, he has not answered.
Your current version is perfectly fine if you're jotting an informal note to a close coworker or friend but if you want to make your sentence a bit more formal, you might consider these recommendations. Here is the full version I recommend:
I've already contacted him about that book and he emailed me saying that he still has copies left. But since then, I've heard nothing. Although I have sent him many emails, he has not answered.
Oh, you may also consider "despite the fact that" instead of "although". They have similar meanings but using despite can be a bit stronger.