You can be issued tickets for up to a year after the incident, however they can't be served upon you through the mail. I would hire an attorney to...

I am trying to get my license back from a start I previously lived in but had some license issues

You have a situation that needs to be dealt with by a lawyer. I absolutely would not not plead guilty just to clear things up.

What happens after I failed to send in my plea or show up in court?

Contact the court by phone. You shouldn't have a problem. If you wait too long, the court can suspend your license.