Do I have legal rights to my parents belongings at death?

I'm sorry for your loss.  If your parents died without Wills, the law of intestacy in the state where they lived determines who has the right to their probate assets.  It sounds like it is you and your brother, along with any other siblings or the children of any deceased sibling.  It sounds like their addition to your brother's home and paying off his mortgage were gifts as the house is in your brother's name, so those are not probate assets.  Their personal belongings are, unless they gave them to your brother while they were living.  So are any bank accounts or other assets that were just in their names.