'Have' cannot be used in the continuous form when it means 'own' or 'possess'. So, you must say 'How long have you had (owned) your car?' 'Do you have a pet?' 'I have a lot of friends'. This is because 'have' with this meaning is a stative verb - it describes a state or condition. 'Have' can be simple or continuous when it is an active verb - it describes and action. This is seen in expressions such as 'have a coffee', 'have a good time', have a shower' and so on. e.g. 'They are having dinner' - describes the action of eating. 'My neighbours are having a party' - describes the actions of dancing, listening to music, eating, drinking, etc.

how long have you had is correct. You can use 'having', but not in this sentence. for example, 'how long have you been having these headaches?'; "We are having a party on Saturday". This could also be phrased as "We are going to have a party on Saturday". I think she is having a nervous breakdown. I am having another cup of coffee before I go to work.