Is it permissible to perform Tayammum for a month due to a medical condition that requires avoiding water?
Tayammum is permissible so long as the above excuse lasts. 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.
What should a person who doubted having missed a pillar of prayer do?
All praise be to Allah, The Lord of The Worlds. The prayer of one who doubts having missed one of its pillars is valid, and nothing is due on him/her since having a doubt after offering the act of worship doesn`t undermine its validity. And Allah Knows Best.
What is the ruling of Sharia on Zina and what is the punishment for the unmarried man who commits this grave sin?
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.
The punishment for Zina (Adultery and extramarital relations) is the same for men and women: 100 lashes for the unmarried to be witnessed by a group of the believers. Definitely, this person has incurred the wrath of Allah; however, he must make repentance immediately, refrain from this grave sin, and seek Allah`s forgiveness. And Allah The Almighty Knows Best.