What was Bibi Umme Kulthum's husband's name?
What was the name of her kids?
I've read on Wikipedia the name of her spouse is Umar al Khattab, why that so?

This a highly debated and contested matter. There are reports that she was compelled to marry Omar, but many of our scholars have disputed that. Either they say the narrations are weak, or that she was forced to marry him (in a long story) but she never ended up living with him. Some have claimed she had children from him, but that’s not correct.
Some also say she married Aun ibn Jafar. It is also disputed whether she had any children. Some say yes while some say no.