Why after on 2-3 days of installing a new battery the car lights will dim and wont start?

A battery is only an electrical STORAGE device; when functioning properly it stores electrical energy.

On the other hand, the ALTERNATOR produces the electrical energy to operate all of the electric components in the vehicle AND sends additional electrical energy to the battery for storage so that the starter can function NEXT time you want to start the engine.

If the alternator is not functioning properly the battery will eventually discharge. That doesn't mean anything is wrong with the battery, it just hasn't been given anything to store. Have a reputable auto parts retailer test your charging system for you.

At this point you should be suspicious of the alternator.