Welcome to the forum!
You are very wise to ask questions. You'll always find someone here who's willing to help you out.
A loose oil cap would have nothing to do with the serpentine belt. Anyone who would suggest this has questionable automotive knowledge.
Typically serpentine belts fail for one of two reasons; the belt is worn out and snaps or the serpentine belt tensioner is worn out and needs replacing.
As for the coolant, you can use any brand you want as long as it meets Toyota specifications. Any competent
auto parts store can provide you with the proper coolant/antifreeze. Many of the discount auto parts stores employ young kids who were fired from a fast food joint the week before, so use caution when dealing with them and get a second and third opinion from other auto parts stores. If you have any doubt with the recommendation you receive, contact the antifreeze/coolant company from the phone number you will find right on the bottle. Once you find a competent person at an auto parts store, stick with them for anything you need with your car.
$130 for an oil change and tire rotation is highway robbery, in my opinion. Possibly they are using solid gold oil filters? An average oil change is about $30 or so and a tire rotation is about $10-$15 in most auto centers. Even only two oil changes in a year would run $260. Good grief! Using the best synthetic oil available, AMSOIL, at the wholesale prices I can deliver to any Toyota Corolla Forum member, that cost is reduced to only about $80. Combined with the improved fuel economy AMSOIL synthetics commonly deliver, most motorists save $100-$200 per year.
I hope this has helped answer your questions.