Yes. In 'Pulp Fiction', Vincent Vega is often in cars and thus associated with car seats as part of the car interiors where his actions and conversations take place.
It's not too complicated. Just go to the car dealerships marked on the map and browse the available cars. Make sure you have enough in-game money to make the purchase.
Selling a car in GTA story mode isn't too complicated. One way is to approach specific in-game characters who have shown an interest in cars before. Also, keep an eye out for special events or missions related to car sales. Just make sure you have all the necessary paperwork and the car is properly maintained for a smooth sale.
First, you need to drive the car you want to sell to a specific location marked on the map. Then, interact with the NPC there to start the selling process. Just make sure the car isn't too damaged or stolen.
I'm not sure specifically what this 'adult baby car seat story' is about as the term is rather ambiguous. It could potentially be a fictional story about an adult who is treated like a baby and has some sort of experience related to a car seat, perhaps in a comical or strange context.