1 and 2 aren't possible.
For 3, you should be able to use the Anaylis board to set up a FEN position, make the moves and use that PGN for the editor. Or just use the insert diagram. But you can't enter the FEN and then paste in some moves.
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When inserting a puzzle, if possible, I would like to know how to do the following things. If anyone knows the answer to even 1 of them, feel free to respond even if you are unsure on the others. I gave some examples however this might be useful, though I'm sure I will find other reasons as I mess with the puzzle feature on this site.
1. Have a puzzle allow you to move for both sides. I can see why this is not a default option, and if it is not even possible to do, that is fine. But if I wanted to make a puzzle to test my memory of say, an opening, I could use this to move both sides. If this doesn't exist, I can make do with one side well enough, but if it does this would be a nice bonus.
2. Have the puzzle hide the outcome. I do not want to know if I can checkmate in a puzzle, but when I insert diagrams and have a move that is checkmate, it will automatically label it as such, even when I try to label no result.
3. Insert a board state, then be able to insert a set of moves into that board state. Say I take a game of mine, and wish to play out a specific position. The FEN of that position, or any other way of setting up the moves, allows me to start there, I want to be able to copy paste a set of moves from a game into that slot rather than moving them one by one. I know I can insert a PGN or FEN individually, but I'd like to use each of them as parts of an overall puzzle set-up.