How do you wire the input of the crossover to the head unit? Can it be wired into the exiting wiring in the door panel?

Does the car need the crossover as the standard speakers are components anyway? Could I just replace the woofer and tweeter?

you need to use the crossover.

You need to find out if the car uses filters on the tweeter as a crossover or if it actually has crossovers of some kind.

The input needs to be a full range signal not interrupted by an oem crossover of anykind