Are these sentences correct?
I have booked an appointment for you to meet with Mr. Smith next Tuesday. Are you fine with this appointment?
or
Are you OK with this appointment?
I find "are you fine?" unnatural.
"Are you okay" is okay.
I'd be more likely to say "Will that work for you?"
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.