1. That's a lot to elaborate, some people fight in NA as Axis, some evacuate from there at once. The proper question is - should Germans be sent there.
2. No, it's not enough. Apart from taking NA and IEA, you need to sink most of RM, land in Albania, take Palermo and Syracuse and only then ITA NM will be around 20%. Depends if they got some premium before, for sinking French ships etc. I don't remember now if ITA bleeds NM turn by turn when Allies occupy Sicily.
3. Check point 2. If allies then take another NM city, esp Naples, then ITA will be on ropes and those surrender/GER control events fire. Ofc taking Rome will kick them out of war even faster, but maybe GER can still assume control. Is it easy to defend mainland Italy? With some Germans it's probably doable, unless Allies really swarm you with AVL and will launch invasions along whole coastline. Italians alone are toast.
4. It does, and quite a lot actually. ITA NM is really fragile.