Is it recommended to stop drinking diet soda?

Yes... . Soda pop contains corrosive acids such as citric, malic, tartaric carbonic or phosphoric which, can remove calcium from tooth enamel. Without protection from the dental enamel, the tissue underneath is susceptible to cavities, root canals & even extractions. Sugar is an additional cavity causing issue, so consider rinsing your mouth after drinking diet soda & soda containing sugar. Water is best.
Yes. Diet sodas, and pretty much all sodas aren't very healthy. Regular sodas contain a lot of sugar and acids - both are bad for your teeth. Diet sodas trade sugar for artificial sweeteners (not too healthy) and still have acid in them - bad for your teeth.
Depends. Depends on what you will replace it with. Water is always the best drink.