How many Star Trek films are planned?

Answer 1

There aren't a 'planned' number of films. The studio will make them as long as they make money. Having said that the studio did announce a fourth ST movie when Beyond was released but after it underpreformed, the immediate plans for a follow up were shelved.

It was reported though, on April 26th 2018, Paramount was developing two new Star Trek movies, although Paramount has not officially greenlit any new movies, it's possible they won't happen but as of April 2018, there are two in the development stages.