Tier 20

Can't say it consistently, but from my experience, I got demoted whenever my score was under 3600 (sometimes even when under 3640 or so), so I'd say that the cutoff line would be there somewhere, although I never paid that much attention to it to actually study the numbers. It depends on the current bonus unit lineup (because people will have at least 3 +10 heroes and then hopefully get lucky with a good bonus unit), but the seasons with limited units tend to have a lower cutoff line, so your score might be enough in the end.

You will probably get in to T20 with a score like that every week, but you won't stay. You're in Tier 19.5 for now. My T20 score is currently 3,640 and I will probably get kicked out if I don't raise that.

100% sure that'll get you into tier 20, Will certainly not be enough to maintain 20 though. That should be good to go back and forth from 19-20 (aka 19.5), only time you may struggle is water week. Everyone will have their stat boosted fjorm and friends.

The threshold is always going up as new characters come out or people gain more merges around your ranking. So keep up with merges on your main team to prevent falling down eventually.