How can I prevent InstantLinks from being automatically exchanged with my site? I would rather receive invitations instead.

Go to Change Settings >> Link Approval Settings and set the Maximum Number of Automatic InstantLinks to 0. If you have already exchange some InstantLinks automatically, you will not be allowed to set this value to 0; LinkMachine will set it to the lowest value possible given the number of automatic links you've exchanged.

This number restricts how many automatic InstantLinks your site will be able to exchange. You will still be able to send and receive any number of InstantLink invitations, without limit.