When the core client runs through Tor and looks for seed nodes. Is DNS still used? And if so, does it go through the Tor proxy too?
DNS can't simply be used over Tor. What it does is it "connects" to the DNSseed names like they were regular peers and gets addrs from them and disconnects, causing the tor network to do the dns resolution and randomly select endpoints. It's not great.
I don't think that Bitcoin Core does this, though it might be a good idea.
There is an open PR on making it use separate tor circuits to reduce the incidence of using the same exit node (but not preventing it: there isn't a way to prevent it without having a very low level interface with tor, AFAIK). I think we previously got sidetracked with discussion on how to avoid breaking non-tor proxies. (The way you get different circuits for different connections in tor is to send different usernames; which doesn't work so well if you're using a non-tor socks proxy and it won't accept a username). I'll be in the next release in any case.