I prayed while I was in the hospital after a bladder surgery, and my urine was connected to me and could not be disconnected that day. I prayed after performing tayammum with my finger because I was unable to stand. What is the ruling?

Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?

The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).

What is the ruling on a woman shaking hands with the brothers of her husband`s father, and not putting on Islamic wear before them?

The aforesaid are strangers to the their brother`s son`s wife, therefore, it is forbidden for her to take off her Islamic wear before them, or to shake hands with them.

What is the best charity to offer on behalf of the deceased? Is it giving food, reciting Quran, giving money or supplicating? What is the best charity to offer on behalf of dead father and dead husband? What is the best continuous charity to offer on behalf of the deceased?

Praise be to Allah the Lord of the Worlds. The deceased benefits from every righteous deed offered on his/her behalf, be that continuous charity, reciting Quran or a pious son praying for him/her. However, the best righteous deed is performing Haj and Omrah on their behalf especially if he/she hadn`t performed that ritual for it remains a debt on them. The evidence on this is that Ibn 'Abbas (Allah be pleased with them) reported: A man came to the Messenger of Allah (PBUH) and said: "Messenger of Allah, my mother has died (in a state) that she had to observe fasts of a month (of Ramadan). Should I complete (them) on her behalf? Thereupon he (the Holy Prophet) said: Would you not pay the debt if your mother had died (without paying it)? He said: Yes. He (the Holy Prophet) said: The debt of Allah deserves more that it should be paid."{Related by Muslim}. And Allah the Almighty knows best.