Lol! I feel you there. Well, I can try to explain if you'd like!!
Notes: Basically private email system, to chat one on one.
Critiques: To request a critique, you need a membership, but basically it is what it sounds like. You'd ask for people to just give their opinion on the piece, and most of the time, you'll notice it's on pieces the artist would like to improve. I'm pretty sure you don't need a premium membership to leave a critique though <3
Mentions: When someone puts a link back to your gallery, or a piece in your gallery.
Bulletins: I want to say those are just little notices from the DA staff.
There's a quick run down of the things that you mentioned XD.
HA! Well, there are quite a few fandom trends that go through DA, and the current BIG one is My Little Pony. You'll notice that there are quite a few pop culture influences, and it's a quick way to get notice if you draw fan art for whatever's hopping XD. You'll notice more come up, the more you watch people/get involved in groups!
Hope that helped!! <3