Yes, people with a dining reservation look for a CM with a tablet at the MK gate who'll be checking to be certain you've a reservation. If you don't see that CM, just ask someone. Once they confirm your ressie, they'll wave you on into the MK.
You'll take the MK Express monorail if it's running for a faster trip. It goes directly to MK, no stops, but may not be running. It's been down a lot lately.
The resort loop train stops at the Polynesian and Grand Floridian and could be quite full, requiring you to wait for the next train. About a 20 minute ride if you get right on, although that one stopped sometimes en route for unexplained delays when we rode it last fall.
The ferry is generally more reliable, but again, at that time of day, you may have to wait for the next one.