Why is the ‘Order’ button greyed out when I try to buy a car on GTA Online

Installing a tracker allows you to see your car on the map. You can install a tracker at LS Customs, or you can get a free one when you store the car in your garage.

A tracked car can still be totaled or stolen. If this happens you are out of luck. Buying full coverage on your car at LS Customs gets around this. If the car is lost or stolen you can call up the insurance company and file a claim to get it back.

Each garage can hold a set amount of cars(between 2 and 10). Most cars you can steal can be stored in the garage. The game is a little restrictive on the high end cars-you have to buy them. I haven't tested it, but I assume you probably won't be able to store the bigger vehicles like semis and cargo trucks either. Physically they are probably too big to fit in the internal volume of the garages(at least the 2-car one I currently own)

Another bonus of the garage is you get a mechanic who can deliver a car from your garage to you anywhere on the map for $50.

If you can't sell the cars to Los Santos Customs because their individial worth exceeds 50k then you are out of luck. You will not be able to sell them anywhere. You will only be able to get rid of those cars when your garage has hit its limit and you will be asked to replace a car. This question and its answer are related to this problem.

On the topic of not loosing cars upon buying a new property, if you buy a property with the same amount of garage space it will not result in the loss of a car.
If you buy yourself a property with less garage space than the one you had before you will loose every car that is in the last few slots. As an example: When currently owning a 10 garage space property the first 6 cars in your garage are important and the last four are the ones you will loose upon buying a 6 garage space property.