Yes you can stay on Mounjaro for as long as you want to, and I think Wegovy as well although there was some guidance in the past that 2 years was advised. I think that’s not the case anymore.
You can stay on whatever dose works for you, as long as your BMI does not get too low (exact number depends on the specific pharmacy that you order from).
Cost depends on dose, have a look at https://monj.co.uk/ for Mounjaro price comparison and https://igovy.co.uk/wegovy-price-comparison-uk/ for Wegovy price comparisons.