haven't tried shooting sports myself with the FZ, but by all i've seen, it should do fine in terms of freezing action, etc. it will defnitely get you a lot closer to the court than the 105mm equivalent zoom you're used to!
as for your second question, the best way to do what you want (sharp focus on a player preparing to serve, for instance, with the background blurred) will be to keep use the aperture mode to keep the lens set at f2.8. that will give you a relatively shallow depth of field, which will help blur the background, especially if there's some distance between the player and the background. since most outdoor tennis courts have at least 10-15 feet, often more, between the backline and the fence or stands, you should be able to keep the player in sharp focus and at the very least put a soft focus, if not blur, the background. how well that effect turns out is in part determined by how close you are to the subject, as well.... it's easier to blur the background if the subject is closer to you than to the background. for your tennis matches, that may not be possible, but try for the closest location and angle you can get.