On mainlines reservations should be available the day before but you might not get the exact train you wish (nor sit together). Look for the train on trenitalia.com and count how many seats are left.
You'll only need 2 reservations for these journeys:
- Naples - Florence (13€)
- Florence - Milan (13€)
There are works around Lago Maggiore so part of your trip will be by replacement bus. For example:
- Frecciarossa Firenze S.M.N - Milano Centrale 10:55 - 12:50 13€
- R Milano Centrale - Arona 13:25 - 14:28
- Bus Arona - Bavona 14:58 - 15:42
And towards Zermatt…
- Bus Bavona - Domodossola 08:10 - 09:09
- EC Domodossola - Brig 09:48 - 10:14
- IR90 Brig - Visp 10:26 - 10:32
- Bus/train Visp - Täsch - Zermatt 10:41 departure
Note that Visp - Täsch is replaced by buses until further notice due to the floods 2 weeks ago. They stick to the regular train timetables but with traffic it's not always possible. Have a little margin.
Reservations aren't a thing within Switzerland.
With questions like these, please always mention the date on which you want to do these journeys.
Italy’s high speed trains are quite frequent, but require a mandatory seat reservation. As do the IC and night trains. Regional trains don’t.
You can make these reservations online in advance via ÖBB or Raileurope (with booking fee), or at the ticket office just a bit before departure. The train you intend to take might be full, but another train an hour later might have free places.
It’s your call and it all depends how stressy you find it 
. I’lld suggest to make seat reservations online in advance in weekends in summer in general, as it can get very busy. Weekdays are usually very okay in summer, save on some popular and infrequent connections (but that’s not the case here).
Seat reservations on domestic trains in Switzerland are not useful and a waste of money, just take a seat wherever you’lld like on whichever train you want to take.
EDIT: I see that @thibcabe already answered in more detail :)
Thanks so much guys!
Do we have to buy/book separate bus tickets for the buses mentioned above or can we just get on the bus with our interrail cards?
If we book seat reservations and change our minds is it possible to change them or would we have to pay for new ones?
Your pass is fully valid on these replacement buses (there are usually trains). No need to book anything.
Checks are unlikely as the main priority is to board the buses quickly. If they do happen, simply show your pass.
Reservation refunds/exchanges depend on the operator. Don't quote me on that but I think Trenitalia reservations are exchangeable but not refundable. However it likely means queueing for an hour at a ticket counter…
I'd check the number of seats remaining and book closer to travel. For Naples - Florence I guess you can be a bit flexible as there are 2-3 trains an hour.
For Florence - Milan a bit less as Arona - Baveno buses run every 2h.
I didn't mention it earlier but the Interrail pass is not valid on the Pompeii - Naples suburban train (Circumvesiana). Buy tickets for a couple of € at a machine, don't forget to validate them if needed.
