IME (broken foot/heel) and wife's knee replacement, the biggest issue is time to get the wheelchair access. It can be quick and it can be longer than desired. So allow plenty of time, especially for connections. When the airlines provide a wheelchair there will be an assistance individual to accompany you who will know how to avoid obstacles and help you thru security
Have never traveled with a personal wheelchair, but there is some risk of damage.
If you need a wheelchair on the plane, it takes a special wheelchair which the airline will provide.
At some airports traveling by electric cart is faster -- you arrange that the same way as requesting a wheelchair
Would suggest contracting the
United Accessibility Desk to discuss options, they are very helpful IME
There is information on the web page concerning customer supplied wheelchairs
You can call the Accessibility Desk at 1-800-228-2744