You should get a screwdriver if your receiving a full set ..
1. If not it's a 1.6mm cut-out (to prevent slippage) screwdriver flat
2. If you want to buy some spare tubes ;
I think they are 2.7mm OD
3. Strap length is dependent on wrist size and how much 'tail' you want, so largely personal preference.
Standard OEM is something like 115/75 and for large wrists 125/90. For extra 'tail' the long part can be 150 + (these are usually by non-OEM or bespoke made)
My preference when I was having them bespoke made was 140/80 but sometimes when I didn't want lots of extra strap flapping around I would prefer 115/75
The standard strap with the 113 is tapered 24/22 at buckle. So if buying a new strap, either get a 24/22 or 24/24 and buy a 24mm buckle
I've lost touch a bit with Panerai lately so maybe I'm a little out here or there. But someone will eventually chip in with facts . . .