1) about 14
2) Shouldn't be too much of a problem. At least one 777 pilot lives in Germany and another in Italy.
3) Generally midday or later at LHR, although there are some earlier ones. At LGW, generally around 9am.
4) You will be on blind lines initially (rostered). Unless you choose to "back to back" (minimum rest between trips, one night in the UK), you will get two clear days (three local nights) before your next trip. On Reserve (standby) which you will do at least once a year initially, you can be rostered a trip after two local nights.