I have 3 Tactics Trainer puzzles to report

I have done 2 tactics trainer puzzles and have found that one of them has a big mistake, while the other one, I don't understand it. 

 
I report puzzles:

0034259 

0033952

This was the solution, why can't white play f3xe

PS: When we report a problem, do they give us it right, after they analyse it, or what?

PS: CHESS.com admins: I reported problem 0022903, but it's actually correct, so cancel my report. Sorry.

Problem #1 - The solution is 3.Rh7 Rf7 4.Rgh1 --- 5.Rh8#.

Your choice, 3.Rh8+ sacs a rook without making progress towards mate. 3...Kxh8 4.Rh1+ Kg8 5.Rh7 {White still has to see Rh7 to force mate!} Rf7 6.Qh5 {Since there's no backup rook, the queen has to take over the role} g6 7.Qxg6 Rg7 8.Qxg7#.

3.Rh7 is superior.

Problem #2. It doesn't matter if he plays 2.fxe4... now that the knight is eliminated, mate is inevitable. If fxe4 then Qg3 or Qxg4 threatening Qxg2#. Now what? Kf1 Qxg2+ Ke1 Qg1#

Both problems are correct... but the finishes are maybe not so obvious.

likesforests also shows why the second problem doesn't continue after Rxe4 but stops there. Only tactics where there's one clearly better move are accepted, and after fxe4 black can win with both Qxg4 and Qg3. If either of them is set to be the right move, then people who chose the other line will complain.

So either the problem has to be deleted (because it could be unobvious that the idea is Qg3 or Qxg4, although most advanced players will spot it, I guess) or the problem stays, ending after Rxe4!

The first problem is correct and your solution is wrong there, as benws and likesforests already pointed out.