Wet dream

Q: When at night we see a wet dream and we ejaculate, is it farz to do gusl afterwards? In winters it is difficult to take bath at fajr and then go to masjid. If after ejaculation we don't do gusl can we offer salaah with just wudhu?

Washing impure clothes in the washing machine

Q:

1) If after washing impure clothes in a washing machine which takes just under 1 and a half hours but a couple of items of clothing still have washing powder residue/white marks on them then are all the clothes rendered pure or would I have to wash them all over again? The cycle has 5 rinse and spins.

2) Also please can you clarify the hanafi madhab regarding tiny impurity. When I use the toilet no matter how hard I try to safeguard myself from urine/toilet water splashes, it seems like very tiny dots of urine are splashing on my under thighs, possible 1 or 2 tiny splash and it is very difficult to wash the area in the toilet itself so this resorts in having a shower waist down every time and takes so much time. Because they are tiny, can they be classed as paak?

3) When having ghusl in shower and the private parts are washed with water and after I use soap on the area to wash it then can I simply wash it off with the shower head without using my hand? Will my ghusl be complete?

Inheritance

Q: My father passed away leaving 6 daughters who are all married and his mother is alive. He also has one sister who is widowed and has children. My question is who are his heirs and how will his house be shared out?

Ibnu Taymiyyah

Q: My question is pertaining to Ibnu taymiyyah. He is someone that deemed the Mongol invaders of the Muslim world to be non Muslim as they didn't rule according to the Law of Allah, he didn't say the same though about his own rulers even though they were not exactly entirely applying sharia and he was loyal to them and never instructed jihad against them. Did he do so on the grounds he thought it is wrong to fight the ruler or did he not deem his rulers as non Muslim in the same way he did the Mongols and if so why didn't he deem his own Mamluk rulers also non Muslim for not ruling by the Law of Allah?