What is the ruling on someone who vowed to fast for two consecutive months, but failed to do so?
He is obliged to fulfill his vow by fasting for two consecutive months, but if he fails to do so then, it remains a debt on him until he either fulfills his vow, or dies. In case of his death, his guardian is supposed to fast on his behalf, or donate food from his estate in return for fasting, but if the guardian fails to do so then, it is all in the Hands of Allah.
Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?
Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.
Is it permissible to combine and shorten prayers at home before traveling?
It is impermissible to combine and shorten prayers at home before traveling because a person is called a traveler once he/she departs the borders of his/her country, and offering prayer that way was originally intended to exempt a traveler. And Allah Knows Best.
Does fasting on behalf of a deceased person permissible?
Fasting on belhaf of a deceased person is permissible, since the Prophet (PBUH) said: "Whoever dies while he still has some fasts to make up (of the days of Ramadan), then his heir (any of them) should fast on his behalf." [Agreed upon]. The previous answer is for making up missed obligatory fasts on behalf of the deceased. But if the fasting on behlaf of the deceased was for performing a voluntary acts of devotion such as fasting....is permissible as adopted by the majority of Muslim scholars and based on the above hadith as they stated "Every good dead intended to be on behalf of the deceased its reward will reach the latter." And Allah Knows Best.