Drywall – put plywood over the drywall on the common wall between the house and garage

I would not waste the insulation on an outside wall unless your garage door was getting insulation. Drywalling has benefits though... First you need to use fire resistant (5/8) in most places in the US for garages, a fully drywalled and painted garage will be deemed nicer by those wanting to give you money for your house, white flat walls reflect light the best, noise reduction... all I could think of.

Small tip if you do this... Run some crosses at like 5 and 7 feet along the wall. That way you have places to nail things without measuring for a stud.

These ventilation bricks were intended to prevent gasoline fumes from accumulating. The CO danger was not the concern as one should only run the engine when the door is open. Modern cars should not emit gasoline vapors in any significant amount, so such vents are typically no longer required.

Additionally, since the study cannot harbor a motor vehicle, such vents just make heating and cooling less efficient, so you would do well to cover them. However, habitable rooms must have some kind of ventilation, typically operable windows. An HVAC system running on fan mode is usually a legal alternative to windows, but windows also provide highly desirable natural light. Which is also a requirement for residences. The usual requirement is 1/10th the floor area for light and 1/20th for ventilation.

BMitch raises a very important issue regarding CO. I've seen offices adjacent to maintenance bays where although the adjoining wall was well sealed to the surrounding structure, exhaust fumes still managed to permeate through somewhere enough to be bothersome to the occupants. Take every measure you possibly can to seal the adjoining wall. It's too easy to overestimate how well a wall serves as a barrier. In addition, be sure to install a CO detector in your study just to be safe.