I believe the legal term is consanguinity, apparently meaning that you are too closely related by blood.
It is not illegal but it may be unwise.
It is illegal in over 30 states in the United States to marry a first cousin. It is doubtful that a green card would be accepted if a person is married to their first cousin.
My Cousin Vinny.
Yes, you can legally marry and have a sexual relationship with your cousin. In some places you can, in others it is called incest and it is illegal; under this law you can't have sex, much less get married with anyone not once removed from you in your family. (First cousins, no, cousins-once-removed, yes.)
Who you can marry depends on the laws of the country you live in and the customs of the ethnic group you are part of.
Yes
He married his first cousin Emma Wedgwood.
Madison
If it is legal where you are, not much if you married your first cousin. You live 'happily' every after or not, as the case may be.
They are your first cousin once removed. It will depend on the laws where you are at. In about half the world you would be able to get married, in the other half it would be illegal.
Procreation is what happens when people have children. There is no special name for it just because people are cousins. In some places it is illegal and may be considered incest for them to marry or procreate.
Your first cousin.