Also, can anyone explain to me why there are so many short positions rather than just buying puts?
Short squeezes are short, temporary events. Even with borrow fees in the range of 30-50% (per year), it's a small price to pay for a short-term play. It's not realistic to expect the general public to continue pouring money into Gamestop stock to keep the price propped up.
Keep in mind that shorts can also exit and re-enter their short positions with high frequency. Not all of the shorting activity is long-term shorting that started <$10
And of course, the original Melvin Capital claims to have exited their original short position. WSB wants us to believe they're lying, but I'm inclined to believe them.