I was able to join >2000 arena .

When i was 2005 yesterday only
I joined in this one
lichess.org/tournament/3MfBnGry

<2000 arena , Actually

if you just crossed 2000 and went below, you can't join <2000 arena's

I think the rule has changed from being one week under the threshold (like it used to be) to being at least 20 games under it. If i'm not totally mistaken, that is...

edit: I'm not sure about that, and i couldn't find any information on the page. So take it with a grain of salt...; )

#3
Yes , But One needs to be below the threshold for a week to join these tourneys
#4 and #5
Ohh !