[COLOR="Blue"]SEAL Part No AP2038837 is the correct seal to repair this leak?[/COLOR]
Yes it is (Item 417)

[COLOR="Blue"]It looks like there is a washer in front of the seal.[/COLOR]
No but there is a push on nut (Item 415) behind it, to hold it in. I would also order one of these as odds are you will mess up the old one when you remove it.

[COLOR="Blue"]Does the pump and motor need to come out to put this seal in?[/COLOR]
No

[COLOR="Blue"]Do I need any other seals if I take the pump and motor out?[/COLOR]
No but you should not have to remove the pump.

Get a shallow pan to catch the water when you remove the seal.
Take note of where the springs etc,. go on the solenoid assembly.
A digital camera picture is good for this.
Remove the small clip holding the lever onto the flapper valve shaft.
Remove the solenoid assembly.
Then the push on nut and the seal.
Take note of how the push on nut is installed, teeth in or out.
Reassemble the rest of the solenoid assembly.

Also a good idea to add a couple quarts of water before trying it. These units do not like to run when low on water, they can burn out the motor shaft seals.