Has Islam made it incumbent on us to give our children particular names?
No, it hasn`t, but it is desirable that we give them good names.
What is teh ruling on thoughtless oath?
One who swears by Allah unintentionally and isn`t determined to fulfill his oath, nothing is due on him. Allah, The Almighty, Says (What means): "God will not call you to account for thoughtlessness in your oaths, but for the intention in your hearts; and He is Oft-forgiving, Most Forbearing." [Al-Baqarah/225]. However, it is dispraised for a Muslim to swear frequently.
What is the Islamic ruling regarding a person finding buried treasure, whether gold or artifacts, and what is their share of it?
If the buried treasure is Islamic, it is considered Luqta (lost property), and the finder must announce it to locate its owner. If all efforts to find the owner fail, the finder may take ownership of it. If the treasure is non-Islamic and consists of gold or silver, zakat must be paid on it, which is one-fifth of its value. And Allah Knows Best.
Is it permissible to move a grave from its current location to another place, for example, from a garden in a home to a cemetery, knowing that the grave has been there for a long time, about fifty years?
It is not permissible to move the deceased from his grave, as this may result in breaking his bones and violating his sanctity. Such actions are not allowed. And Allah Knows Best.