Do I have to have an appointment in order for them to take a look at my cellphone?

Yes

Yes, you do.

Yes. The evaluation is quick and if it does need a fixture it can be done there, do expect to wait several hours. Since they do handle a great volume of persons a day.

Possible because they are always busy. Call them because I do not work for Apple.

I think no. There is a possibility that you have to leave it there