Add people, set their hours, and say which services each one performs.
Availability comes from your people, not from your services. A service nobody performs, and a person with no working hours, both show a customer an empty calendar with nothing explaining it.
You can also add equipment here — a chair, a machine, a room — as something a service needs. A service that needs one is only bookable while one is free.
Closing for a day or a holiday is done under Quote & Booking Settings › Blocked Times rather than by editing hours, so your normal week stays intact. One entry can block a single day or a whole range, such as a Christmas shutdown.
Yes — the booking form offers your people by name. Equipment is never offered; it is picked for them.
Block the day out under Quote & Booking Settings › Blocked Times. Bookings already made for that day are still there and are not cancelled for you.