Is Zakah(obligatory charity) due on rented property, and how is it calculated?

Zakah isn`t due on the rented property itself, but on the saved income from that property if it reached Nissab(minimum amount liable for Zakah), and a whole lunar year had lapsed over saving it.

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.

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.

For passing time, my friends and I have called a famous diviner. She told me that somebody had cast a spill on me not to get married for the rest of my life. I didn`t believe her, but I can`t forget her words. How can I protect myself from such thing?

Praise be to Allah the Lord of the Worlds.

Dealing with diviners is forbidden and what you are suffering from is due to your having consulted that diviner. Have trust in Allah and ask Him for forgiveness, but rest assured that whatever Allah has decreed will take place. And Allah The Almighty Knows Best.