Can the friend buy a car in gta 5 and mod it and give it to me if he removed the cars insurance so I can keep it

If you park a car in the garage, it will be saved there. Your standard car will always be available nearby if it is not in the garage. Parking in the garage will save that car and you can access there unless you left it somewhere else.

Taken from the manual:

Player characters can own any vehicle in [GTA V] as long they have appropriate storage for it. To purchase a new car they must first own a garage ... If a vehicle is destroyed it will reappear at any residential property that the character owns with a garage (note that this does not include safe houses). If an owned vehicle is lost, stolen or abandoned, it will be impounded. To retrieve impounded vehicles the character must pay a find of $250 and collect the vehicle

I think this is for cars bought in the Rockstar Store. The first one you get for free by joining the Rockstar Social Club. Cars bought on a dealers website are only delivered once to your garage. For the marina it is a bit different: There is only one slot and you can choose (by pressing LEFT on the D-Dad) which vessel to spawn there. You can do this an infinite number of times. This also applies to the helipads and hangars. You can only spawn vessels bought on a dealers website before.