Tor does not use the same exit node for everything. The Tor Browser actually uses a security feature that makes sure it does not share the same circuits with any other program that uses the Tor client.
Sites you visit while using Tor have a relatively easy time to find out that you are using Tor. This is because your connection comes from one of the 1000 or so Exit Relays in the Tor network. You can not "overcome" this while using Tor, all Exit Relays are publicly known. One thing you could try doing is contact the site and ask them nicely not to block ...
Well, privoxy and polipo are basically even: they both have filtering systems inside them, both are HTTP-to-SOCKS tools. In the last beta of tor you have a HTTPS proxy embedded in tor itself, so I'd rather recommend you to use an embedded one. To do so you should add HTTPTunnelPort directive to your torrc like this:
To fix all the DNS issues like that I do recommend you to use a local resolver configured for using Tor as a transport, but serving your system as usual. I'm using ISC Bind, works like a charm. Don't fprget to edit /etc/resolv.conf and so forth.