You didn't answer 1,2, and 4. 2 doesn't really matter but still. I'm guessing you're using Java2D as well.
For a video game you're going to want a seperate inputlistener class to store all your input listenening functions. I'm not going to show you how to do this or program the input for you, you can find all that online very easily. This isn't the classroom anymore, you're not copying down stuff from a book.
As a side note try and make your code a little more organized. Group similar calls together and comment your code if you like. It helps, trust me.