I have bought a pack and was wondering if my son can use this on his account.
Yes. Has long has your account is set to “This is my home Xbox”, everyone else on the same console can use the cars in the car packs.
So, if he uses his profile on a friend’s xbox (and what if they have DLC) or gets his own xbox later, he just sees the non DLC cars?
Hopefully somebody will correct me if I’m wrong here, because I haven’t actually used my profile on another Xbox, but I think what happens if the friend doesn’t have the DLC is that the son would be able to see the cars that he’d bought, in his garage, but would not be able to use them.
If the friend has purchased that same DLC, I’m inclined to believe the son would be able to share that DLC on that console also.
Not having personal experience though, I will also say I’m not positive on anything beyond my first post. Probably best to seek confirmation on everything in this post. 
Thanks
If you were to buy your son another Xbox YES he can use everything you download, games or add ons. All you do is set his consol as your home consol and your consol as your sons home consol. Reason being if you set your Xbox as your home consol he would need you signed in on his consol to use downloads. This I a great feature which means if you download say forza you only buy it once where as you would need 2 copies on disc. As me and my son have xbox ones I will never buy another disc.