I was just there a couple of weeks ago, so I can answer one question...no, you don't walk through either park to get to DTD. It's out in the open and free, except for parking. If you do drive, you can park and get your ticket validated at the movie theatre or a restaurant for free parking.
Not too sure about your other question...we stayed at the DL Hotel, and it was my first time there, so I'm not all that familiar with the surroundings and the roads (I remember Harbor Blvd, but not exactly where it is). It is a pretty congested area though and lots of things are close together.