Citation Excel pilot reported cabin pressurization and cabin door malfunctions during cruise flight. The flight crew diverted to an appropriate airport.

Narrative

In route to ZZZ and deviating for weather build up over the state; Captain and myself had a 'CABIN DOOR' amber annunciation and 'MASTER CAUTION'. We silenced the 'MASTER CAUTION' and began running the manufacturer's abnormal checklist for 'CABIN DOOR' annunciation in-flight. Part of the checklist called for cabin pressure control to be set to 'MANUAL' and cabin pressure altitude set to 9;500 feet.In the process of establishing 9;500 feet of cabin pressure altitude; a 'CAB ALT' red annunciation and flashing 'MASTER WARNING' illuminated. I immediately donned my oxygen mask; set to 100% Oxygen; set microphone switch to 'MIC OXY MASK'; and began a descent at 200 KIAS (required by 'CABIN DOOR' checklist). Cabin pressure indicated stable at 9;500 feet cabin pressure altitude; so we did not initiate an emergency descent. The Captain began the 'CAB ALT' checklist at this time; we diverted to ZZZ1; and [requested priority handling]. The Captain briefed the passengers on the state of emergency and diversion airport.During the descent; at an altitude between FL180 and 14;000 feet MSL; the 'CAB ALT' annunciation extinguished. At 12;500 feet MSL I removed my oxygen mask. While the 'CABIN DOOR' annunciation never extinguished; the rest of the flight continued safely and without note.'CABIN DOOR' ANNUNCIATION - SPECULATION:During post-flight inspection and while communicating with the Director of Maintenance; it was identified that a door pin indicator would not center. It is presumed that during the flight that pin or sensor and indicator failed. Which caused the 'CABIN DOOR' annunciation.'CAB ALT' ANNUNCIATION - SPECULATION:It is presumed that the adjustment of the aircraft's cabin pressure altitude may have briefly exceeded 10;000 feet. However; the indicated cabin pressure altitude was verified by both pilots several times; as this was the initial assumption. The gauge indicated 9;500 feet. We now speculate that the gauge itself is not accurate. We believe this is supported as once cabin pressure lowered to approximately 8;000 feet; the 'CAB ALT' annunciation extinguished.FUTURE PREVENTION & CORRECTION:I believe that the 'CABIN DOOR' annunciation cannot be prevented or corrected in-flight. At the beginning of the flight; the door pins were seated and verified by the green door pin indicators; the handle was stowed; cabin door lock lights were extinguished; and the 'CABIN DOOR' annunciator was extinguished. This event was at a time in-flight of no note; and with no perceived threat that would allude to the impending illumination of the 'CABIN DOOR' annunciator.With only speculation of the 'CAB ALT' annunciation; I cannot provide opinion on future prevention or correction. However; if it was due to an inaccurate gauge; then the gauge's accuracy ought to be corrected.