Can we make our own puzzle and publish it??
Unfortunately, if you're planning to put it on Chess.com, you're out of luck. I don't know how they make their puzzles, but they don't dip into other peoples' games. However, if you would like, you can create your own puzzle and post it in a forum. Here's how.
1. Click the game board icon above the forum post. It should bring you to a gameboard screen.
2. Click "set up position" and set up your puzzle.
3. Click the "moves" tab. Make the moves that will solve your puzzle for BOTH teams. Just click on the pieces on the board and move it like in a chess game.
4. Click the "theme" tab. Select "puzzle".
5. Click "insert". Your puzzle will be posted.
I hope that this teaches you how to make a puzzle, although, unfortunately, you can't publish it.
Your games will sometimes be published as puzzles in Lichess.org I think, but not in chess.com