F or L visa invitation letter

To visit a friend or friends in China, live at their home during stay. I must get letter of invitation from them?(each one?) Does it need to be physical letter or can they provide e-mail inviitation? How about the signature or official stamp(I do not know what this is). Places to visit is not known in advance, mostly stay with the friend(s) and visit local places over several months.

Arrival/departure dates are based on plane ticket. How specific does invitation letter need to be with these(can provide a date range, or must be specific days arrive/depart?). It looks like I must have booked flight already before apply for entry permit?(I would rather visa be approved before buy plane ticket if possible).

Is there example invitation letter somewhere?