To answer (some) of your questions from my experience (3 years instructing PPL full time in the SW of England before moving on last month);
Realistically, your income is going to be very low and not liveable on if you teach full time PPL. The school I just left paid around about £20/flight hour. Some FT FIs were on a small retainer, others were not. This worked out around £ 1300-1500 per month in summer, and £700-900 per month in winter. Before tax, although if you got yourself a good accountant and were paid self employed then you'd not pay very much to HMRC. Hours wise I did about 400 a year.
Demand in my experience varies a lot from school to school; I know of schools that are very busy at the moment with another school 50 miles away which is going through a slack period. Obviously weekends are more popular and winter cuts down on flying.