Got em. Nice puzzles.
Very hard studies

What's missing from this thread is the name of the composer of each study. Who can name all four? Who can name even one?
No one replied to this, so I'll answer my own question. All four studies were composed by the same person.
1. A. Wotawa, Deutsche Schachzeitung #330, 1959
2. A. Wotawa, Deutsche Schachzeitung #2245, 1944
3 . A. Wotawa, Deutsche Schachzeitung #1990, 1937
4. A. Wotawa, Deutsche Schachzeitung #1993, 1937

Here is another hard study. I didn't include the solution. Instead of just saying "I solved it!" you need to post your solution.
White to play and win.

In the 4th one the solution is actually wrong! The moves are the following:
1.Re3 b2 2.Bf5 gxf5 3.Rb5 Rxb5 4.Re6 fxe6 5.g6 h4 6.g7+ Kh7 7.g8=Q+ Kh6 8.Kf7 b1=Q 9.Qg6#
Correct. But if Black sees the game is lost and wants to prolong it out of spite, it could end like this.
In a composition, though, the game is over when one side has a clear winning advantage.

the fourth one is an invalid puzzle, although gxh4 is winning Kf7 and g7+ are checkmating in 4 moves
This is an invalid comment. The fourth one is not an invalid puzzle. The mistaken posting of an invalid solution does not make a puzzle invalid.

the first few moves are correct but the puzzle solution wasn't supposed to be extended after that because there were multiple solutions
This was originally a composed endgame study, for which there is a codex of rules. It was presented here as a puzzle. There are no official rules a puzzle solution has to follow.
The minimum requirement for an interactive puzzle challenge is that it should be solvable. Not just after numerous tries but in a single run when all your moves are correct, i.e. permit you to reach the goal. When you use a puzzle engine like chess.coms which only interacts on 1 solution line you can not request the solver to choose between 2 correct moves - since he would be guessing not solving. In those cases the puzzle is flawed as presented, even though it may have been a fine puzzle or problem in a different puzzle environment.

The minimum requirement for an interactive puzzle challenge is that it should be solvable. Not just after numerous tries but in a single run when all your moves are correct, i.e. permit you to reach the goal.
A study which stipulates "White to play and win" often leads to a position in which White has a clear winning advantage. At that point there may be multiple ways to achieve the win. Does that mean endgame studies are not suitable as chess.com puzzles? Must they all be directmate problems in which only one line leads to mate in no more than a specified number of moves? Should the posted solution be required to give a winning line against every possible move by Black at every turn?
This (once there are duals) is where aborting the solving process comes in. Though you might want to display a sample line demonstrating the remainder of the win, you shouldn't bother the solver with finding those follow-up moves.
But in fact the chess.com puzzle module is terribly primitive. I can literally think of hundreds of improvements to raise puzzle solving to a decent experience. One is already in the Lessons module which allows the interface to ask for an alternative line without flagging you red for a different good move. That of course should be made part of the standard puzzle interface. And there are so many others like two-sided play, multiple solutions/solution lines and automatic counterplay in solution parts. Some years ago I played on a Go puzzle interface which had some of these features but is still a long way off from the toolkit you visualize when you sit down and think about it for a while.
Examples from experience:
I made an endgame study with a minor dual in a king walk but unambiguous before and after it. Though it takes away some of the value, the remainder of the study is still valid. As a puzzle I don't want to make the solver decide on the dualed move. Instead, I would like a tool in my puzzle toolbox which would automatically provide the desired choice (or a complete detour) and then resume the solving process after the move was gifted in the diagram.
Many endgames can be prolonged by making repetition loops in places. I want a tool in my box simply blocking to play the moves that enter the loops. Not as an error but simply to help the solver avoid wasting his time or getting red-flagged for no good reason.

When I first encountered chess.com's approach to presenting puzzle solutions, it irritated me to be told that what I knew was a perfectly good move was incorrect. In time I came to accept its limitations, and see it more as a friend who has some personal foibles but can still provide some enjoyable companionship. It clearly could be better, but is not likely to change, and I no longer expect it to offer more than it has to give.
Still, I liked hearing your ideas about how a puzzle interface could be made to do all the things we wish it could do.
In the Ice Ages the bear hunter next door and the ice picker on the next glacier are our best friends but after a few millenia I'd like to move on the civilization
Btw, the future for the civilized puzzle toolkit looks bleak when I consider the level of our puzzle posters. How many of its brilliant instruments will they ever use?
It took my 27 minutes and 41 seconds to solve them all, when I tested all my answers at the end, no mistakes. Good puzzles, I really got into it
These puzzles are not easy and that is a fast time. One day you may be a world solving champion. That title actually exists!