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.
Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
Is it permissible to thin the eyebrows or remove them and draw in their place?
Thinning the eyebrows, removing them, and drawing in their place—known as Namas—is prohibited. The Prophet (peace be upon him) cursed those who do it. And Allah Knows Best.
Is Aqeeqah due on the miscarried embryo?
No Aqeeqah is due on the miscarried embryo.