How to interpret the Reform Programs tab in Prison Architect?

Solution 1:

by your points:

What do the different colored boxes (green, yellow, black) indicate? Prisoner type, concentration, or success estimate?

Black - signed up for the program, yellow - en route (as far as I observed), green - 'in class'. Black during session - unable to reach (lockdown/solitary)
Also there's a lighter shaded grey which indicate maximum program capacity. I.e. you have 15 desks in classroom - you will be able to distinguish 15 and 5 extra - for potential increase in classroom capacity.

Does the bigger box indicate the session leader (teacher, psychologist, foreman, doctor, etc.)?

Exactly like that.

What do the red lines mean? Why are some longer than others?

Progress since start (% program completed). E.g. Parole has 1 session, so It's progress bar will fill up from start of session till end. Multi-lesson programs, like kitchen safety & hygiene will fill up as sessions take place.

What does the "Reschedule All Programs" button do?

This one is not 100% clear to be, but simple explanation is that the game tries to reschedule the programs automatically to maximize 'employment' - number of prisoners signed up to all programs given your constraints (manually fixed programs, available rooms & staff etc.) - by reshuffling the programs and reassigning prisoners between them.