I understand that for the first year of the student plan I pay £15.49 per month and then the next year I pay £21.91 per month but do I pay this for every month that I'm a student or does the price increase again in the 3rd year? Or is there a cap on the number of years I am eligible for the student plan?
You are eligible for the student plan as long as you meet the qualifications of being a student. The price remains the same for the second year and subsequent years (though it could change if Adobe adjusts their pricing). It is just the first year that has the added discount.