Could you please highlight the ruling on offering a sacrificial animal as a ransom? Can the person who offers the sacrifice eat from it and feed his relatives from it?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

If the person offers the animal sacrifice seeking thereby to draw closer to Allaah, the Exalted, through feeding the poor and so on, then such an act is recommended, just like other righteous acts that bring one closer to Allaah, the Exalted. If the person vows to offer a sacrifice when adversity befalls him or the like, then it is incumbent on him to fulfill his vow and offer the animal sacrifice to its beneficiary, exactly as identified in the vow. In such a case, it is impermissible for him to eat from that sacrifice, unless the common practice in the country where he lives allows the vow-taker to eat from his vowed animal sacrifice.

However, if the person is offering the animal sacrifice as a voluntary act of worship and did not vow to offer it, then he is entitled to distribute its meat in the way that he wishes and he may eat from it and feed his family from it as well. 

Allaah Knows best.