I\'m finally starting out with unit testing, having known that I should be doing it for a while, but I have a few questions:
(Not quite in the same order as your questions)
If the full test suite doesn't take too long, you should always run it complete. You often don't know which side-effects may result from changes exactly.
If you can combine speed tests with your favorite unit testing tool, you should do it. This gives you additional information about the quality of your changes. But only do this for time-critical parts of your code.
From Wikipedia: "A unit is the smallest testable part of an application."