Is there a limit to the number of times you can buy and sell the same stock in the same day? Do you have to wait to buy the same stock again if you sold it recently?

There are no legal restrictions on trading frequency. However, be aware that if you take a loss on a particular sale, the wash sale rules preclude you from deducting that loss on your income tax if you buy the same stock within 30 days of taking the loss (that's 30 days before and after).