Yes - once appointed, a co-opted member has exactly the same status as an elected member.
The composition of the finance committee is a matter decided by the whole council. Presumably you are implying that the co-opted member was not appointed to the finance committee by the council.
The finance committee (just like a council meeting) must be open to the public, including council members who are not members of that committee. Except in the case where a specific motion is passed, for good reason, to exclude the public.