Family trees traditionally have ways to show genetic relationships (children) and legal relationships (marriages, adoptions...). Step-brothers and step-sisters can come about in several ways, and some of those ways produce half-brothers and half-sisters. It really depends on the specific relationships, both genetic and legal, between the people.
As far as 1st cousin once removed, that's your first cousin's child, and you can do that by adding a child to your first cousin.