Water leaking in front driver floor area
 

I have a 2003 Sebring Sedan LX. Water is getting in the front driver floor area. Doesn't look like it's coming in under the plastic or rubber in the door frame.

I think it might be coming in through the door. In the attached picture, after running a hose over the car for several minutes, the bottom of the plastic trim, where the screw is, was wet. Just near the front. From how the carpet is getting wet, I am suspecting it is about the same area as this.

My question is: Is it normal for that part of the part to be wet or is this the source of the leak?

There should be a weatherstrip running around the door opening that the door presses up against to seal out water spray. Take a good look at the weatherstrip and compare its condition to the other side of the car to make sure it's not damaged, missing or out of place.

Leaks can be hard to precisely locate. Water will run down due to gravity, so the point of the leak will generally be above where the water gathers, but water can also move sideways so the leak isn't necessarily directly above the point where it winds up.