Yes, they both affect your SERP and PR. The 400 is bad request error and 404 is not found (which means the first one doesn't respect all the rules and the second one the page isn't there), and search engines don't like them.

I am not familiar with all the details of ownership, but as far as I am aware, you have the author rights over your own art work and they have to buy them out before they can trade mark it. But then again, it is a shady area and given they have their own in-house legal team, they might have used some alley or loophole that only they knew about in order to get your logo without having to buy your rights (like the lack of invoice to prove ownership, for instance - did you at least have a written request for the logo or sth?).

I am not an expert and author rights law is a very tricky one, so you should make sure you have evidence you did the artwork and then maybe search legal counsel.