Ghusal

Salaah becoming qadha due to not making fardh ghusl after becoming baaligh

Q: If a male becomes baaligh by having wet dream and ghusl becomes fardh on him, but he doesn't know that in Shariat you have to perform ghusl after having a wet dream. So he keeps praying with just making wudhu and after 3-4 months of his puberty, he comes to know that ghusl becomes fardh by wet dream. So are all his prayers in these 3-4 months counted or does he have to make qadha?

While offering these prayers again will he make intention of praying qadha prayer or will he make intention of repeating the prayer (I'adah)?

Taking long to make ghusal

Q: I get frequent wet dreams. The problem is that it takes me about 30 mins daily to do ghusl. The main problem in ghusl is washing my feet which can take upto 20 mins because my feet has dirt inside the lines so I rub them with a pedicure stone until they are gone.

I am moving to a hostel for educational purposes and there I will have only few, maximum 5 mins for a bath as there will be a communal bathroom. Plus, the temperature can be 0°c or below too so I can't take a long bath. What do I do as I am becoming depressed due to this thing?