Please see This link for definitive answers and remember to always check with a lawyer if you are unsure.
Also understand the difference between "free as in beer" ($0) and "free as in speech" (which is what the GPL is actually about)
My understanding below:
1.) Yes, perfectly fine to do this
2.a) Forking closed content, generally no unless you have the Copyright to that closed source in which case you can release it again as Copyleft/GPL. Once you let the Cat out of the bag it stays out though.
2.b) Yes, not a problem
3.) Grey area, the GPL typically is strict about being part of or even linked into (as a library) with non-GPL compatible code but I forget the exact details. You'd need to check the license of the propriety software and the GPL itself. There are also slightly less stringent licenses such as the LGPL and Apache licenses which people tend tall fall back to if they want to be "safe than sorry"
4.a) Any modifications _must_ be made public and given away for free use (free speech concept).
4.b) There is nothing wrong with selling it though (for example you can buy Linux CDs!)