Is there somewhere online I can play chess tactic puzzles and redo them whenever I want? I do tactics on lichess but it doesn't store my puzzles. Is there somewhere that stores all my tactic problems so I can redo them? I feel that would be better to develop pattern recognition. Thanks in advance.
If you have a premium membership on ChessTempo, you can create problem sets with spaced repetition, which is one of the advanced options under problem search. If you select this option, the site will show you both new puzzles and puzzles you've already solved. You'll see puzzles you've gotten wrong more often, and if you get a puzzle right a few times, you won't see it as much.
Lucas Chess, which is a desktop program and free to download, also includes sets of tactics puzzles for training using spaced repetition.
I don't know of a specific tactics site that stores all your previous puzzles so that you can redo them. However, to develop pattern recognition you don't need to do the exact same puzzles over again - doing different puzzles with the same type of tactic / concept is just as good or better.
It's better to get a variety of examples for one tactic / concept, since it would cover more of the possibilities you can face in a game. Just doing a few puzzles many times wouldn't be as good, since it doesn't cover enough of the types of positions you may run into during a game.
If you want to see full solutions immediately after you get a puzzle wrong, try Chess Tempo. It shows you the full solution after you finish and let's you play through it.
I do problems on Lichess, and they do save at least the last 15 that you've done. There are little boxes for each of these in sequence under the current problem diagram that you can click on to bring up the old problem diagrams. The boxes are either green or red according to whether you have solved or failed the problem.
As Larry Coleman Said, a premium membership on ChessTempo will allow you to do that. I would like to add that Lichess also implemented this feature in 2016. Without you knowing it, it repeats problems that you got wrong until you get them right. See this blog post