Wudhu

Wudhu and ghusal for a person who has severe scalp acne

Q: I am a woman who has severe acne on her scalp. This has been causing me extreme distress, especially with regards to purity and showering. The pimples on my head are infectious and filled with pus. They pop all the time and when they pop they release pus/blood/liquid for usually two-three days (this is called "weeping", common for acne pimples). It is almost impossible to catch a time when there are no "weeping" pimples on my head. The only time I get to wash/shampoo my hair is when it is fardh for me to make ghusl (usually once/twice a month). I am afraid to wash my head otherwise because that would only spread the impurity coming out of the pimples all over my body. However, it is becoming extremely difficult not to wash my hair.

My hair is long and my scalp becomes very oily quickly and it makes me feel disgusted. Not washing it often seems to be worsening my acne, as well as making my head itch like crazy (and itching it just pops more pimples). There doesn't seem to be any effective medical solution for scalp acne, I've tried a couple things but none of them worked. This situation is really stressing me out. Can I just shower whenever I want to even if the pimples on my head are releasing impurity? What do I do about the impurity going all over the rest of my body?

Fardh and sunnah acts of wudhu

Q:

1. What are fard acts of wudhu? If I want to wash my face and there is some sweat on my face, can I make my hand wet then wipe my face or washing my face is required?

2. Also, if I were to wash my arms or face, normally I wet my hand and touch the tap to close it and wipe my face after touching tap. The tap was wet due to me closing it, so is my wudu valid since my hand had mustamil (used water )?

3. Also when doing masah, if my hand touched my wet face and that water also came in doing masah is my wudu valid? (Here also mustamil water)

4. Is doing wudu in steps compulsory or not?

5. Is it compulsory to complete the wudu before the hands and face get dry?