Does the clipping of nails nullify ablution?

No, it does not, and it is preferable to wash the hands afterwards.

When is Istikharah (guidance prayer) Du`a offered, before Tasleem (saying asalamu alikum warahmatu allah wa barakatuh to end the prayer), or after it?

It is offered after Tasleem.

I have been married for five years. My husband has two sons from his first marriage. Nevertheless, I took care of his children, and gave birth to a baby boy who is now three years old. Unfortunately, we keep fighting all the time; sometimes over his two sons and sometimes over his family. If I serve his family members and praise them, he treats me kindly. If I don`t, he turns my life into living hell. What should I do?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Spouses should live with each other on a footing of kindness and equity. In your case, constructive dialogue is the best course of action. We advise you to be patient, commit your affair to Allah and ask Him to help you. We also recommend that you seek the help of the people of goodness and make them fix things between you and your husband. If all attempts for reconciliation fail then go to court, but we remind you that a problem, which could be solved with a beautiful word, is no problem at all, so praise family and children and try your best to win their hearts. And Allah The Almighty Knows Best.

Does offering Udhiyah (Offering a Sacrificial animal at Aid Al-Adha) avails from offering Aqiqa?

Offering an Udhiyah doesn't avail a person from offering Aqiqa because each of which is a different act of worship. And Allah Knows Best.