"How is it possible for the state to suspend trial by jury in matters involving incarceration?"
A defendant can waive that right and go for a bench trial, or a legislature can insist only bench trials apply to certain things like traffic tickets. In the case of administrative law, a legislature creates an agency with rulemaking powers, then gives it judicial powers to enforce it's rules. So, essentially, only the agency rules apply, and they are isolated from the legislature and the state courts. Remedies can only be had, by suing the agency, or by changing the composition of the legislature to one that will eliminate, or change the rulemaking powers of the agency.