Is it a condition that the meat of the Eid sacrifice should be distributed in order for the sacrifice to be accepted by Allah?
The poor and needy should be given from that sacrifice , even if it be a small portion,(One kilo for example) as raw meat so that they would cook it the way they want. The remainder of that sacrifice is either distributed, eaten, or offered to people in a banquette .
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.
Does touching one's wife invalidate ablution?
Touching the wife according to the Shafi'ee's doctrine invalidate husband's ablution. And Allah Knows Best.
A man break his fast once during Ramadan and he already have an expiation of fasting for two consecutive months. He fasted for a month and passed away. Is it permissible for his sons to fast the remaining month equally?
Fasting for expiation must be performed consecutively. I advise his children to feed sixty poor people, giving each one half a kilogram of rice or its monetary equivalent. This is because if a living person is unable to fast, they are required to feed sixty poor people, and death constitutes an inability. And Allah The Almighty Knows Best.