Amalfi Coast + Puglia + Rome

Guys, I’m going to Italy next month (June) and since the trip came up last minute, I still have a lot of questions. 😬

The initial itinerary would be:
12th: departure
13th to 16th: Rome (3 nights)
16th to 21st: Amalfi Coast (5 nights)
21st to 23rd: Capri (2 nights)
23rd to 29th: Puglia (6 nights)
29th: return

1) Do you think this number of days for each place is reasonable? Or should I increase or decrease any of them?

2) Is it worth including Matera and/or Ischia?
If so, as a day trip or staying overnight?
If staying overnight, where could I cut days to fit them in?

3) On the Amalfi Coast, is it better to stay in Sorrento, Positano, Amalfi, or Praiano? Or should I split the stay between two bases? Which ones?

4) In Puglia, I’ll most likely split the trip into two bases. Which ones would you recommend?

5) In your opinion, what’s the best way to get around within each place?

Context:
Couple’s trip.
We like beaches/beach clubs, beautiful scenery, cultural immersion, walking around charming town centers, good restaurants, and some nightlife (bars or even a little clubbing).
We want to avoid stress (if possible lol).