Does the clipping of nails nullify ablution?

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

What is the amount of Zakah (obligatory charity) due on articles of merchandise?

The amount of Zakah due on articles of merchandise is (2.5%) of each article`s value after a whole lunar year had lapsed.

What is the ruling on giving my mother a gift at "Mother's day", is it Halal or Haram?

Praise be to Allah the Lord of the Worlds.

There is nothing wrong with doing that as long as it isn`t done in imitation of the disbelievers. And Allah The Almighty Knows Best.

What is the expiation for breaking fast due to being on a journey, or being sick, or being in a state of menstruation?

No expiation is due on the aforesaid categories, but they are obliged to make up for the missed fast. However, if any of them failed to do so while being able to, and the next Ramadhaan has come, then making up for those days is incumbent on him/her , and paying the ransom as well. And Allah Knows Best.