Is it possible to destroy your own car and get money from the scrapyard for 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

The cars are spawned at your big garage (colorful garage icon on map) for every character. One should note that these cars are spawned only once so make sure you bring them back in one piece.