Water on floor

Try going at this yourself. At least for the easy part.
With th door open, look for any tell tale signs of water leakage. IT may not be coming from the door but maybe the windsheild or elsewhere.

Is it possible that the water is coming in from the a/c running and not draining to the exterior?

While your in the car looking, have someone on the outside spraying the door area starting from the bottom and going up. I would suggest using short quick bursts that are not with high pressure, like how rain isn't high pressure.

This may also be from a drain plugged that is in the wiper transmission trougth area.

There are folks that specialize in water leaks if nothing is found. Dealers will often hire out someone like this.
If you can find them, you can deal directly with them.
Body shop and independents may also use them. Call around and ask if they can refer you to someone such as this.