I placed my hand on the Quran and made an oath to avoid doing a specific matter, but the devil seduced me. What is the ruling on this?
You are obliged to pay an expiation; feeding 10 poor and the cost of feeing one is half JD. And Allah Knows Best.
Should one fulfill his vow of donating an animal to the poor and needy with one sheep although he had repeated the vow several times?
Each vow has to be fulfilled, and repeating the words of the same vow for confirmation renders its fulfillment obligatory as one vow. As for multiple vows, they have to be fulfilled as well.
What should one who forgot to offer the second Sajda during congregational prayer, and remembered it before the end of the prayer do?
All perfect praise be to Allah, The Lord of The Worlds. Whoever forgets a pillar of prayer while in congregation must follow the lead of the Imam, and after the latter offers Tasleem, he should offer one Rakah, then perform Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.
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.