Do handicap guests get any preference on wait times and if so what proof is required?

For sure you need to check in at city hall. There are different "packages" persay.

Persons with handicap can bypass the normal lines with separate shorter ride entrances. I noticed that they are usually labelled.

No proof was required, you must check in after going through the gates.

Yes. You must visit City Hall or any information booths. No proof is required, but most tell him or her reason if your handicap. Then you can get a return time without standing in line