Can I connect a 12/2 wire to a 10/2 wire to operate garage openers?
You can, and the combo requires a 20A, single pole breaker

You can always use larger require than the minimum required by Code for a given circuit ampacity -- given that the 2017 NEC now requires a 20A circuit for garage receptacles, your plan of extending this circuit with 12/2 is fine.  It will require a 20A, single pole breaker of a suitable type for your existing panel (we'll need to see the labeling on the panel if you want advice on what to buy for a breaker, though), and you'll need to use a torque screwdriver when installing the new wiring (with your main breaker turned off, of course) due to the requirements in 110.14(D) (again, new with the 2017 Code).

Garage receptacles (save for ceiling ones) need to be GFCI protected

The general garage receptacles will need GFCI protection as well -- I would run the wires to the garage door opener receptacles first and then to the first general garage receptacle's location; that way, the GDOs don't wind up on the GFCI rather needlessly while the general receptacles can all be protected by a single GFCI located at the first general garage receptacle box that has the incoming hot + neutral connected to the LINE side, and then you can take the tape off and connect the outgoing hot + neutral to the other receptacles to the LOAD side, thus protecting all the garage receptacles with one GFCI.