Is the marriage contract considered valid if concluded at home by the marriage official (Ma`zon)?
Yes, it is valid as long as it is registered at the court.
Can the Christian widow whose married from a Muslim become an heir of his?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
A Christian widow can`t inherit her Muslim husband because their religions are different. And Allah The Almighty Knows Best.
Is it permissible to offer the Eid sacrifice in a non-Muslim country?
Eid sacrifice is permissible anywhere, and Islamic Sharia hasn`t determined that it should be in an Islamic country, but poor Muslims should be given a share in order for it to be valid since it is an act of worship. A portion of that Eid sacrifice should be given at least to one poor Muslim, and if that wasn`t possible then the one offering it should consume it along with his family.
Should the father command his ten-year-old daughter to wear the Islamic dress?
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.
The father should order his daughter to put on the Islamic dress once she turns ten, in order for her to get used to it. And Allah Knows Best.