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.
What is the ruling on making up for missed fasting after the second half of Sha`ban (the month before Ramadhaan)?
One is obliged to make up for missed fasting before the start of next Ramadhaan, and regardless of offering it during the first, or the second half of Shab`an. This is because the prohibition mentioned in the Hadith is for offering absolute voluntary fasting in the second half of Sha`ban. And Allah Knows Best.
What is permissible for the husband to do as far as having sex with his wife is concerned?
The couple are free to enjoy each other sexually provided that they don`t do it during menses. It is also forbidden for the husband to enjoy the wife from her anus.
What is the ruling of Sharia when husband kicks the wife out of his house without a lawful excuse? Moreover, in such case, when she stays at her parents's house for several months, is she allowed to claim maintenance through a Sharia court?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It isn`t permissible to kick wife out of house save for a valid reason since Almighty Allah Says (What means): "O ye who believe! Ye are forbidden to inherit women against their will. Nor should ye treat them with harshness, that ye may Take away part of the dower ye have given them,-except where they have been guilty of open lewdness; on the contrary live with them on a footing of kindness and equity. If ye take a dislike to them it may be that ye dislike a thing, and God brings about through it a great deal of good." [An-Nisa`/19]. In addition, it is the duty of the husband to provide for his wife and children in kindness, and this includes food, garment and residence. Moreover, dialogue and supplication are the best means for solving marital problems; however, the wronged party may resort to court. And Allah The Almighty Knows Best.