How many invites can I make?

There is no limit. The point of invites is that it allows you to declare all the times at which you are willing to play. You must, however, be prepared to play at your invite times as others will be able to book a firm court with you. So don't set an invite just because you may be around - that's too weak. You need to be prepared to play.

Invites incur no penalty if you don't get taken up on them simply because you never reserved a court that would block others from using it