I am not sure anyone fully answered your questions about what to expect from the person who pushes your wheelchair. Normally this person will wheel you right through customs and immigration, if you need to stop at a restroom you may make that request and the pusher will take you there. If you want to stop at a restaurant or club room they will take you there and leave you. Normally you will be given a card and a number to call when you are ready to leave for your gate. Occasionally the wheel chair pusher will not only deliver you to the luggage pick-up, but may also help you located your bags and help you to the curb.
One of the best things for me about being in the wheelchair is the ease with which I normally pass through security. The person who pushes your wheelchair will be directed to a security location and he will move directly to the head of the line. You, along with whom ever you are traveling with will immediately enter the security process. I have prosthetic replacement joints and always set the metal detector off, so I just proceed immediately to the pat down area. The person pushing my wheelchair usually supervises my belongings on the conveyor belt and brings them back to me. We experienced that same "front of the line" service at custom and immigration points when we travel internationally.
Having said this, you may experience the occasional airport or airline that does not do a great job of this. In some airports my request for a wheelchair has been addressed by pointing me to a wheelchair. Once in a while, an airline employee has suggested that my husband push my wheelchair. This is not a good option for us. He has our carry-on luggage, boarding passes, my ID and his ID, and he is also disabled and cannot push the wheelchair without causing pain to himself. Worst of all, he will never accept the front-of-the-line opportunities so we stay stuck at the back of the line.
The person who pushes your wheelchair is likely a minimum wage employee, and I think he/she deserves a good tip. I generally base that tip on the amount of time the wheelchair pusher is with me, and the amount of services he provides. If someone picks me up at the plane, takes me through customs and immigration, manages my luggage during customs, re-checks my luggage and delivers me to my gate I tip $15 to $20.
If someone picks me up at the check-in desk and negotiates me through security and delivers me to the gate I normally tip between $4 and $8 depending on quality of service. Indifferent or unpleasant people do not get as much as those who are personable. A month ago as we were moving through the terminal at 5:30 am I asked my husband to stop at a Starbuck's. The man pushing my wheelchair decided we would all stop at Starbuck's. While my husband got our beverages my wheelchair assistant kept me entertained with stories from his years playing basketball. He then took me to the gate and made sure that the GA knew I was there. He then gave me his card and told me I could call him on his cell phone if anything happened and the gate changed or I needed help the next time I was in the terminal. I gave him $10!
You should certainly not feel guilty about using a wheelchair. I have had mobility difficulties for nearly two decades. I can walk for short distances, transfer from chair to seat and manage some stairs. When I received my last knee replacement my doctor said that I should imagine that the knee would provide X number of steps, and I should make sure that everytime I took one of those steps it was an important step for me. In other words, I should not waste my steps. For me, moving great distances in an airport when I do not need to constitutes a waste of precious steps.
Initially I felt a little guilty when we always moved to the front of the line, were boarded first on the plane and got those other little perks society reserves for the disabled, but that guilt passed quickly. If I were in a normal line I would slow the entire process down for everyone behind me. I no longer feel anymore guilt about using a wheelchair in the airport than I do about using my disabled placard when parking my car in a disabled parking place.
Order a wheelchair and save those precious steps for precious moments!