Ponies main resource production is Power. Power is used by dairies to increase milking rate for the cost of power usage.
Ponies don't have limits but instead have Stamina. All pony activities require stamina. Stamina can be recovered though in a Livestock Stall.
Ponies include all genders. For breeding, there is a stallion flag that can be set via the farmhand terminal.
Yes a pony can complete circle and power quota each day.
No. Pony role has no effect on cow and bull grade.