Yes, possible. These are regional trains, no seat reservation needed (or possible).

I doubt they will be full. There are more than enough trains between all your destinations. If you take the high speed train, reservations are needed. When do you plan to travel?

You can get your seat reservations for Italian day trains here (3 EUR for Intercities, 10 for High Speed Frecce trains):

I would like to travel on the 2nd June to Florence and back and 3rd June to Pompei and back. What trains will be full - high speed or local train to Pompei? Thank you

If these are the only trains you will take, it might be cheaper with normal tickets than buying an Interrail pass.

Fridays are usually a bit busier. But again, there are many trains on those connections, if there’s one full or sold out, there are others a bit later or earlier where there is place.