The answer to all three questions is yes, although it may add a level of complexity to the workings of the council and I wouldn't recommend it. It becomes particularly complicated if the Chair assumes either or both of these roles, as the model standing orders and financial regulations are based on the standard practice of a paid employee. Section 112(5) states that:
"Without prejudice to the provisions of subsection (1) above, a parish or community council may appoint one or more persons from among their number to be officers of the council, without remuneration."
The position of RFO has no special status in this regard, so any councillor may be the Clerk/Proper Officer/RFO.
As somebodyelse has stated, these positions must be unpaid in such circumstances and if a councillor resigns to take up a paid position, they cannot be paid for the first 12 months.