The others have explained the meaning. Note that your sentence is more typical of British English; in America, we would usually say “call the shop” or “call the mechanic”. In America, “garage” usually has its original meaning (a place where we can park — compare to the French garage / (se) garer).

"Call the garage" It means you find the phone number and call the auto repair facility closest to you. Once you tell them your car will not start then most likely they will send a tow truck to pick up your car.

This is a great question. You take your car to a repair man which is usually in a garage. So it's referring to taking your car to the repair man or calling the repair man. However, I would just say I'm taking my car to the mechanic. If you have anymore questions feel free to book a lesson. I have availability this week. See you soon.

That means to make a phone call to a place where vehicles are repaired to ask for help.

call the car shop or towing service.