A fascinating line of questions!
1. I would think it wouldn't be common, but given that the Cobras have a very different point of view than many other Clans, it could stand to reason that a Reservist who was doing Cloister service might get nominated for their efforts by a grateful/scheming upper-level member.
2. The Cobras are stated to keep their whelps in sibkos until their 21st birthday, with a heavy emphasis on learning to serve The Way as well as on fighting. If that held true for freeborns as well, I'd be inclined to think that there wouldn't be a significantly higher level of freeborns versus Trueborns in reserve units. Perhaps a bit due to inherent cultural biases, but not horribly so.
3. While I agree with your thesis that lower ranking warriors would make up a good amount of the reservists, my thoughts on this go back to the descriptions of Cloister service. The warrior seems to be seconded to their Cloister for training and service, and the reserve system seems custom made for this. Any warrior wishing to take time to do their religious duties would be able to step away without worrying about damaging the strength of the touman. I'd imagine that there is a good amount of upper-level Cloister members on reservist duty at any given time to account for this.
4. I'm not certain on this one, as I don't know if we've had a lot of examples on Cobra military culture to draw from. There's a certain dark comedy to the idea of a Black Adder-esque warrior who manages to weasel their way into active duty, only for another warrior to transfer in and bump him back into the reserves.
5. The Cloud Cobras are nothing if not political, despite their protests to the contrary. Reservist #7 might be able to jump to Reservist #2 by joining the Cloister of their Star Colonel, or becoming the coregn of an ambitious Star Captain, etc.
6. Ooh, maybe? I'd feel pretty bad for the opposing commander who let their Cobra opponent defeat them by getting away with that. Definitely seems like one of those shrewd bidding tactics that get talked of in other Clans.
7. Hmm, again I want to say maybe. Up against a hated foe like the Coyotes? Most likely not. ("But I am a warrior! See this patch?" "Too bad, technician. Keep loading those ammo crates!") Other Clans might see it as a bit of a bonus, netting yourself more trained personnel than you otherwise would in a Harvest trial.