1) I'm not sure you should ever get a "permission denied" error for root, but here's a
guide on setting permissions. You also might add your user to the "admin" group, which should give you a few more rights to edit certain files or run certain programs.
2) I don't know, you could make it so you can log in as root I guess. But this is bad practice and shouldn't really be done, so I'm not going to figure out how to do it. You can install
gksu or similar that should let you run apps as root though.
3)
Here,
here, and
here.
And just in case you're interested, here's a couple of good Debian specific websites.
http://aboutdebian.com/
http://www.debianhelp.co.uk/index.php