For the invite question:
When you say invite, do you mean invite him because he does not play the game yet and you wanted to send him a link to download the app? Or invite as in he already has the game and you wanted to challenge him to a match?
If he doesn't have the game yet and you were using the Facebook friend invite list, we have discovered some issues with certain people's Facebook permissions and have put in a fix to resolve this that will be in the next version.
If you were just trying to challenge him to a match, could I please have some more details to try to help you out? What exactly did it do when you tried to challenge via Facebook and via username? Also, what is your friend's username? If you would like to email that information to me rather than post on here, you can email me at firstname.lastname@example.org
For the random invite question:
We have had such an overwhelming influx with users that the random invites from people have become quite a bit overwhelming as well and we failed to anticipate how many people would want to play random players in comparison to just friends. We are working on resolution to this right now and will be getting it out in the next few weeks. It will involve a much better random matching engine, that will only match up with other people looking for random players as well as the ability to opt-out of random play if you only want to play friends.
In the meantime, you can open the match and press Decline to decline the match. We have also implemented a faster auto-resign to clear games off everyone's dashboards.
Thanks so much for bringing these to our attention and thanks for your patience.
We will stay in touch and let you know when things are resolved!