Faraaidh and Sunnats of ghusal

Q: After one has a shower, is it necessary to then perform wudhu in the normal way for salaat? Or is wudhu deemed to take place when one has a shower? 

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?

Q: If I have olive oil in my hair and I make wudhu/ghusl afterwards, is my wudhu/ghusl accepted?

Q: I was not able to take out one or two strands of pubic hair during shaving. I still made my ghusal for haidh. Was my ghusal valid?

Q: While making ghusl, I forgot to wash the inner part of my navel with my finger. Is the ghusl valid or do I have to repeat the ghusl? Is rubbing inside the navel necessary in ghusl?

Q: Can a person gargle and make istinshaaq before sehri ends and thereafter make ghusal? 

Q: Can a person face his back towards the Qiblah while bathing?

Q: If I do istinja in my shower with the water from my shower, will the floor in my shower become najis? If it becomes najis, how can I purify it?

Q: Which direction should we face while taking bath?

Q: On average how many minutes should a:

1. Fard ghusal take?

2. Sunnat ghusal take?

And how should we get rid of doubts when taking a ghusal?