You have to know why certain moves work and others don't. To improve at chess you must be able to use the tactics if it occurs in your own games. Doing tactics without understanding why a certain was chosen over the other possibilities will not improve your chess tactical ability. I think that 200 tactics problems a day is a little overwhelming. Try 10-20 problems/day and study the alternative moves.
Hope this helps.
If you can solve a tactic puzzle in less than a minute it's too easy and won't help you much beyond warming up for actual puzzles. Repetition is important to engrave the patterns of tactics, but it sounds like you've got these down and it's time to move on.
Try finding some hard puzzles that take something like 10 minutes to solve just one. Not only are they more satisfying but you'll notice improvement in calculation and tactical patterns.
How exactly should I go about doing tactics problems to improve my chess? Is simply solving them enough? Or should I study all the alternative moves and see exactly what's going on? Because right now, I do around 200 tactics problems every day, but all I do is solve one and move on. Should I maybe shorten that number to around 25, but actually study each problem deeply?