Playing it out against the computer, it seems pretty winnable from there.

Black's rook doesn't want to give up the e-file under any circumstances and let your king get out of the little box it is creating.

First, play Qc7+. If the king moves, you have a free tempo. If Re7, then Qc4+ will give you that tempo (either the king moves or the rook blocks and gets pinned). Either way, you can repeat this a few times and get your king to f3. You may even want to play g3 just to tighten things up.

Once you've done that, your plan is to get the black king into a suboptimal position. You want him to give up the e7 and f7 squares.

The best and easiest way seems to be manuever around your queen to h7. Black can't really stop that without giving up the e-file.

Once you do that, it's pretty easy to get black into zugzwang. You put the queen on g6, and black's rook needs to stay on e6 in order to both protect the pawn and keep your king pinned in. Black's best try is probably just to shuffle the king around, but then you play Qf7, meaning that if the rook wants to stay on e6, then black's king has to keep touching it. He'll have to play Kd5, and when he does, you play Qd7+, forcing Ke5 to save the rook. But that gives up the e-file and lets you play Kd3 and black ends up in the mother of all zugzwangs.

Once the king gets gets out of the f-file box, it's a pretty simple matter to march him around until he can help, and black can't hold everything. You either win all the materials or you force him to trade down into a lost king and pawn endgame.

In the first one Rb7 with Nd6 or Ba5 trapping the queen.
In the second one Qf7+. If Kh7 then Bf5+ Kh8 Qg6. If Kh8 then Qg6 and Bf5 looks enough... but maybe there is better.

For the 3rd one Qg5 looks obvious but winning a piece

The 4th one looks like it is meant to be Qe1+ and Bf1 fails to Bc5. But Kg2 instead of Bf1 and Bc5 Qf3 looks like good defense for white. So I'm not sure. Bc5 it looks like there's just N2d4 (g7 threats). If Rxd6 then there's always pawn takes.

For the 5th one I think Nxd5 doesn't just win a pawn, it wins a piece (or the exchange and a pawn)! The test is Bxd5 Ng5 Bxg5 Bxd5! (NOT Rxd5) and now black is screwed. If Qc7 then Rxa8 Bxc1 Raxc1 and black has lost the exchange and a pawn. (NOT Rxd5). If, after Nxd5, Nc6, then Nf6+ wins the Queen for Rook and Knight. If Nxd5 Kh8 the Nf6 threatens h7 and the queen. White is won!!

In the 6th one, Nxc4 looks good enough

i'm thinking Bh6

Black cannot break through on the K-side because white has two squares (e2 and f2) that correspond to g4. But the threat of going there might rule out certain queenside squares for black.
When black's king appears on d7, we must move to b4. b5, a5 and a4 would be too far away from the k-side, and on other squares we lose b6.
If black's king goes to e6, we need to move to c3. Thus we can deduce the following:
e7 corresponds to b3. f5 corresponds to d2. f6 corresponds to c2. f7 corresponds to b2. g6 corresponds to c1. g7 corresponds to b1. e8 to a3/c3, f8 to a2/c2.
and thus g8 to a1 (because on Kf8 we must go to a2 or c2, on Kg7 to b1 and on Kf7 to b2).

Solution: Ka1. Black to move would win by Kf7.

here's the ms paint solution to the problem:

Slow game vs. strong opponent, which I won hahahaha, but the computer doesn't like it but what does it know?