My name is Lucy and I'd be happy to answer your questions today. I'm sorry to hear about your friend's situation.
Since they are not married, if her name is not on the title, then he is the owner of the property and she is essentially a tenant. Without a written lease, she would be a month-to-month tenant, which means that he can ask her to leave at any time, as long as he gives her written notice at least 20 days before the end of the month. RCW 59.18.200. That means that, if he gave her the notice before the 11th, she needs to be out today.
As far as what she can take - everything she owned before they moved in together is hers. It's up to the two of them to divide joint purchases. Since they're not married, a judge isn't going to divvy it up for them - unfortunately, unmarried couples don't get the same protections under the law. If they never had an agreement, she's entitled to roughly half of the items they purchased together. If she's taking the children with her, she can also take their personal items, clothing, etc.
Child support and custody are really different issues. If there's no court order that says otherwise, when she leaves, she may take the children with her. She can respond to his petition by asking for sole custody
. The judge will look at several factors to determine what is in the best interests of the children. He'll consider that the father has another child that he favors over these two, and he'll consider if the father has basically thrown his children out of their home on 20 days notice.