To answer your question, yes - you can park at the parks for free on check in and check out days. You will receive a parking pass when you check in.
I gotta agree with Deb & Bill on using the Disney Transportation System. It is nice to put the navigating in their capable hands at the end of an exhausting day at the parks. Especially since you will be at MK. Rather than queing up with everyone going everywhere for the monorail or ferry and then doing it again for the trams, you can just get on the dedicated bus for your resort with other guests.
The only way I would recommend not using the Disney transportation is if you are at a park on a check out day. That way as soon as you get to the car you can head home. Oh yeah, use your own car to go to waterparks too.