Someone else will need to answer the question about closing down the 5k course; despite strolling the course in an hour I was not at the back of the pack and some of the character lines I passed were 15 minute waits.
Post race it is up to you. In January I showered and dressed for the park at 2 am - yes, that means I walked the 5k in jeans - as I had a breakfast reservation at Magic Kingdom. For the 10k and full I wore running gear and then went back to the room to shower. Some people go to the parks in their running gear, a lot go back to their room to change, some bring a gear bag to check with post race clothing. It is a matter of personal preference. Keep in mind that for the 5k you will be getting on a bus at 3:30 am, standing around until after 4, and then standing in your corral from 5 am until start (typically 6:15 ish for the last corral). Allow at least 45 minutes to clear the finish chute and get to wherever you are headed (hotel or park).