Can siblings get married to each other?

While cousin marriage is legal in most countries, and avunculate marriage is legal in several, sexual relations between siblings are considered incestuous almost universally. Sibling incest is legally prohibited in most countries worldwide.

What happens if a brother and sister have a kid?

The risk for passing down a genetic disease is much higher for siblings than first cousins. To be more specific, two siblings who have kids together have a higher chance of passing on a recessive disease to their kids.