Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
What is the ruling on visiting a deceased's grave and supplicating Allah for him by his wife? Is the reward of reciting verses of the Holy Qur'an reaches the deceased?
There is no harm on visiting graveyard by woman with the intention of piety so long as they are dressed in accordance to the Islamic teachings. We ask Allah, The Almighty that the reward of reciting the Holy Qur'an on dedicated to the deceased reaches him. And Allah Knows Best.
Are phone conversations between the two sexes permissible if for consultation, and within the limits of good manners?
Such act is impermissible since it renders hearts corrupt, and could lead to forbidden attachment. Allah, The Almighty, Says (What means): "and follow not the footsteps of the devil." [Al-Baqarah/68].
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.