My name is ***** ***** I would be happy to provide general information regarding your question. I am sorry to hear of the unfortunate position you're in due to your brother's actions.
Let me begin with your first question.
Your brother's actions would constitute Identity Theft (or at the minimum, Impersonation).
Most areas of Identity Theft require that the person who stole the victim's identity use said identity in order to obtain anything "of value" (i.e., a loan, credit cards, cash, etc.)
However, a provision of the Identity Theft/Impersonation law also makes it a crime to use someone else's information in order to avoid criminal prosecution (which can be inferred in your brother's circusmstances as if he were arrested in the past and used your identity/SSN by giving it to the police, that information will appear on your own background report (whether it be a criminal background report or credit background report).
So, it looks like one way or the other (with the goal to avoid criminal prosecution or with the goal of obtaining credit/loans, etc), your brother gave certain information that did not belong to him to an entity or organization.
Legally, only two things can be done. First is criminal prosecution. This entails reporting your brother's actions to law enforcement, who then conduct an investigation. If they believe probable cause exists that your brother committed a crime, it would be turned over to prosecutors for charging.
The second option would be a civil lawsuit against your brother for fraud. The can only be an option if you have incurred what is legally called "damages." Damage is the term for "harm" committed against you as a result of your brother's actions (for instance, if he took out a loan that has never been paid back and your credit report has been ruined, etc).
I will pause here for a moment to allow you to ask me any question you may have on what I have provided before moving onto your second question.