How reasonable are fast food restaurants when it comes to requesting days off?

employers are very reasonable as long as you are honest, REALISTIC, and live up to your commitments...

do not put on the application that you can work open to close 7 days a week when you know that you can't be at work before 9am or can't work on Thursdays......

realize that the more available you are the better chance you have of getting hired but do NOT lie, communicate openly and honestly, as soon as you have a problem TALK to management about it, and by all means live up to your commitments. if for some reason your availability changes talk to your manager about it, but you must understand that when you change your availability they may not need you it depends on the staffing situation what changes have taken place etcetera.... mangers are also much more willing to work with good employees then with bad ones...

you do NOT need to (and should NOT) put on the application that you need a particular day off (NON-recurring one-time occurrence); BUT you must discuss that need if/when you are interviewed.

do NOT wait until you are hired to have that discussion, concealing such information is not how you start out a new job (and keep it).

Be up front

I can work pretty much any hours between _am and _pm, the only day I would have a problem with that is __, that day I am already committed to something I can not get out of, so that would be the one day I would really hope to be scheduled off.

you need to let the prospective employer know what hours you are available to work(in fact many applications actually have this as a question to complete)

and you need to let them know up front that you will need to have a specific day when you cannot work

you can't. they tell you when you work and that how it goes.