Sex charges are very serious. You face prison as sell as being classified as a sex offender depending on the offense. You should hire an attorney ASAP. You should also not waive speedy trial till you consult an attorney.
An "no information" means the prosecutor dismissed the case before formal charges like an information was filed. A "nolle prosequi" means the prosecutor dismissed or dropped your case after formal charge or information had already been filed . Both mean the case against you was dismissed.
Most private attorneys file a written plea of not guilty & waiver of arraignment, therefore the court waives both the attorney & defendant's appearance. You should not be concerned. It is a common practice.
The statute of limitations for a theft is usually 5 years. If it is alleged that you stole >$300 then it is a felony theft. The state usually requests a warrant for a felony charge. That could be why you never received a summons in the mail.
If the state can prove that your brother broke into someone's house, then he can be charged with burglary of a dwelling which is mandatory prison (maximum 15 yrs). The pawning offense is called dealing in stolen property which also carries a maximum 15 years. Your brother needs to hire an experienced attorney ASAP! Good luck!