I selected the wrong grade of gas, but then I quickly pushed the correct button on the pump. Does it change after it starts?
If the pump changed the fuel grade it was pumping you'd see it in the price. My gut sense is that it won't change – too unusual a use case and too much cause for confusion.
That said, don't worry about it. If you put in a higher grade than you need, that shouldn't be a problem at all. If you put in a lower grade then you might notice some pinging and it would be a good idea to fill up with the proper grade as soon as you can.
No, not where I live. The other selections are not available after choosing one and the pump will not change while you are pumping.
To change, you would have to complete the current transaction, then start a new one with the grade selection you originally intended.