Is your friend a premium member? There are 50,000 of the problems but some premium members can do hundreds a day and have done them enough to memorize them.
Can a player be rated 1700 blitz and 2600 on tactics trainer?

He is a premium member, motm.... although I don't think he's doing hundreds a day. I don't think he's done as many attempts as me.
I have found that I've started to remember more puzzles the more I've done. But still no 2000!

Got 1 today which was exactly the same one as puzzle I had a year ago. Remembered it and solved correctly. I really don't know what you're doing, because your blitz is great. Maybe more patience?
I know a guy 1850 in standard(250 games),1400 in blitz
1450 in tactics (around 500)..
and it's very normal to me..

One reason you are having a different experience than your friend could be your backgrounds in chess. Many really good blitz players have a strong background in slower time controls.
As for your on success at Chess Mentor, maybe you are trying to think like a blitz player when you do the problems.
By this I mean that in blitz there are things you just would never do in slower games because of the high rate of people overlooking tactics and weaknesses. It may be that some moves are habit, so you automatically want to play them.
What do you think?
A friend of mine here on chess.com has these ratings. It made me wonder what I'm doing wrong... my blitz rating is similar but I can't get near 2000 on tactics trainer.
What's the secret??