I just recently started taking a look at the forums and noticed that tournaments existed, which is awesome. However, I apparently have missed all the entry dates for the tournaments. Is there a way there can be notifications sent out for tournaments or create them in app?

I believe the devs intend to implement a tournament mode sometime in the future, and I'd assume something like what you're asking for will be a part of that. The tournaments on here are unofficial and organized by players, so I don't think we can do any more than we have.

Check in on the holiday tournament, there's a short wait list but the games almost started, I dunno if there's a spot left or not. Maybe PM the organizer.

I've made a list of all the tournaments:
viewtopic.php?f=5&t=1176