The correct answers are He is playing tennis with Sarah next Tuesday, He is meeting his study group on Wednesday afternoon, and He is going to the dentist this Friday.

We do not use prepositions (in, on, at) before the words next, this, last, or every (e.g., next Tuesday, not in next Tuesday).

For a specific day plus a part of the day, we use on (e.g., on Wednesday afternoon).

Using the present continuous (is playing, is meeting) is a very natural way to talk about fixed future plans!