Hi, Sherri! I'm so sorry about your foot surgery, but rest assured, you can maneuver Walt Disney World with your wheelchair and not have to worry too much about logistics!
You can indeed leave a wheelchair outside of a restaurant. When you arrive at the podium, you can simply tell them you are going to walk to your table and ask where you may leave the chair. It will be easier to push aside if you fold it, but usually, they will put the wheelchairs in the same area as the strollers.
If I were you, I would take advantage of the Guest Assistance Card. You don't need a doctor's note, but if you have one, it may better assist the cast members in knowing how best to accommodate you. The card should be able to help you avoid having to stand so long in lines, offer you access to wheelchair entrances where they are available, or sometimes even offer you entrance through a Fast Pass line so your standing time will be reduced.
There won't be any difficulty using the monorails, the ferry, or the boats. If you are in your wheelchair, there may be a specific car you will need to ride in that is designed to accommodate the chair.
Have a wonderful vacation!