Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
What is the ruling on working for a company that manufactures cigarettes?
All Perfect Praise is due to Allah, The Lord of The Worlds
Working for a company that manufactures cigarettes is forbidden because smoking itself is forbidden, so its production, selling and circulation are forbidden as a result since they aid in committing sin, and whoever aids in that is like the sinner himself. And Allah Knows Best.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
Is it true that if a ritually impure, or a menstruating woman visits one who is in confinement, harm will be inflicted on the latter, or her baby?
This is completely wrong and unfounded piece of information.