What i'm thinking is not a class that you choose in the class options but rather when you enter an air vehicle as a pilot you would have your current class swapped out for a default pilot class which would offer bonuses but when you get out of said vehicle you would still have this class.
If there are specialized marines in piloting in the lore I think they should you let you skill up piloting in detriment of something else (let's say instead of melee combat bonus). I just dont know if there are any, I dont recall any mention about it in the books I've read.
God no. The requisition system used for special roles and vehicles won't allow you to pull vehicle after vehicle, because you simply won't have the resources available. Having Pilot as a dedicated role is a bad idea.
No it wouldn't, it will allow everyone to spam transport vehicles. A Rhino is much more resiliant than a Space Marine, if you have 1000 Rhino's charging a base because you allow them to be pulled infinitely there is no way of stopping it. This is also a bad idea.
It would be good if you became a good pilot as you wouldn't die easily so you would have a class dedicated to a vehicle you are good at
As far as pilots go, Techmarines are generally pilots of everything but a rhino and I think rhinos are tacticals or assaults.
There is no locked class system as far as I'm aware so you can probably jump in and out of them as you wish.
Vehicle spam will ruin this game. Vehicles, whether they be Rhinos, Thunderhawks or even Drop Pods, are a precious resource that cannot be easily replaced.