Italy is amazing, I could happily go every year.
In the tourist areas you won't need any Italian beyond thank you and hello/goodbye. In less touristy areas, less English is spoken, but the people are generally lovely and helpful and you will get by with a few words from a phrasebook/app and some pointing.
The public transport is generally good but is a bit area specific. The south doesn't have a great train service and you need to use buses on the Amalfi. The bay of Naples train is slow and basic. Around Rome/Milan/Florence the trains are great much nicer than the UK, fast and easy to use.
My advice would be not to try and do too much. If you only have a week don't try and go too far, do one area well and go back next year.
I would say either spend the week in Rome and do it justice or stay in Sorrento or on the Amalfi and do Pompeii, Herculaneum, Vesuvius and the Amalfi coast. If you want to chill out and do beaches then the latter, Rome is quite busy.
Venice is lovely but it doesn't fit with your other priorities and is probably easiest done as a city break on its own. It is also miles from the other places you fancy.
You could try and split your time between Rome and the bay of Naples to fit in Pompeii and Herculaneum but I think you would feel rushed. There is so much to do in Rome.