1.
Yes, you are right, one of the places to look is the kernel bug tracker.
Searching the Linux kernel mailing list as well as the subsystem-related mailing lists could also be helpful but is probably more difficult.
2.
The main kernel mailing list is here. You can find subscription instructions there.
3.
There is also a very useful information about contributing to the Linux kernel and the development process in general in the kernel docs: see Documentation/development-process.
4.
If a bug has already been assigned, this does not always mean the assignee is actually going to work on it anytime soon. It may mean that (s)he is just responsible for a particular subsystem.
So, I suppose, if you find the assigned bug you would like to fix yourself, you could contact the person the bug is currently assigned to and offer your help. If a mailing list address is used instead of a personal email address of the assignee, you could write to that mailing list, ask if anyone already works on the bug and, again offer your help.
5.
One of the ways to see if the bug has been fixed is to try to reproduce it both on the kernel it was reported for and on the latest kernel variant for a particular subsystem. Its is not always easy but still can be very useful to get you into the development process.