You know your questions are nearly so open-ended and could take pages to explain in detail?
Do not disturb the gray composite, the back-plane coating is conductive but not as good as a conductor will be - you will need to solder the conductor tabbing on in three spots or so on each of two conductors matching the ones on front but only tacked in place with smallish 3/16" inch solder points, without leaving a mountain of solder on the outside.
You really need the tab ribbon conductors, they lay flat to keep stresses on wafers down AND their coefficient of expansion for heating cycles is mild enough they usually won't self-destruct in time. A way I've used to solder tabbing on is use the straight edge of a culled PV wafer to hold the tabbing down, and run a hot iron down the work to activate the solder paste and melt the solder - then release the straight edge clamp after its cooled.
A good no-clean solder paste has a flux that is non-corrosive. Traditional rosin based solder pastes will need cleaning as they usually have a petroleum jelly base, the 91% rubbing alcohol usually will get the burned rosins off but its still 'polluted' with the jelly base so may not the the best solution.
If I missed something, everything, anything get back on and ask questions