Appointment scheduling nomenclature

The "individual time period during which I work" has a specific name in English: shift. Cambridge mentions it as describing the time worked:

a group of workers who do a job for a period of time during the day or night, or the period of time itself

I worked the last hour of my shift on autopilot.
His shift starts at seven o'clock.
She's just finished a 13-hour shift at the hospital.
Studies revealed that doctors were routinely working 15-hours shifts.
As her shift finishes, mine begins.

The resourcing software I used to work on called the recurring group of shifts over a week the shift pattern. Wikipedia calls it a shift plan, rota or roster, although Google finds images for shift pattern. Different members of staff can work different shift patterns; and your shift pattern might change from week to week. It's simply the pattern of shifts that you work. This means that availability is fine for the time during which you are actually available.

The time at which a single appointment starts doesn't have a word in English. The appointment is the meeting which takes place, "I have an appointment at 10:15". So we would say "The appointment starts at 10:15." If you wanted to call it something, appointment time or appointment start time would be entirely understood.

The word schedule for the whole thing is a good word, although my subjective impression is that it's only recently come into widespread use (perhaps with computer diary/calendar software). "Let me see if I can fit your appointment into my schedule".