1. It's hard to tell. Probably yes - compared to other European capitals, apartments in Budapest are cheap (even when taking into account the difference in incomes). However, I've noticed that over the past 5-6 months, the really great deals are gone; I was thinking of buying a second apartment and visited a few last September. Not only that all of them were bought up quickly, I haven't really seen any deals that were nearly as good since then. Still, medium and long-term, I don't think you're losing money if you buy a good apartment now.
2. Well, Hungarians are conflicted about some of the areas of those two districts as well. I know people who live in the 7th, in the Keleti/Garay area, and like it, while others would not consider living there. From what I've seen, none of those areas are really terrible - perhaps more than anything, you need to make sure you're in a 'good', civilized and well maintained building, and you'll be fine.
3. On the Duna House page you can read their monthly reports, where they publish data on the real estate market; they also report on those margins. If I remember correctly, the average is around 6-7% (negotiation margin). So offering 10% less is not insulting to anyone, but you have to read the circumstances well... if the owners just dropped the asking price (to a very reasonable level) they're unlikely to accept 10%.