Hawker 750 flight crew reported receiving a low altitude alert on approach. Flight crew corrected altitude and completed the approach.

Narrative

While descending for the RNAV Runway XX approach into ZZZ; we had a brief altitude excursion. I was the Pilot Monitoring and Second in Command for the flight. We were cleared for the RNAV XX via VOR; ZZZZZ; Straight in and told to maintain 7;500 ft. to the VOR. As I was looking down programming the FMS; I looked up and noticed that the Captain had descended below our altitude assignment of 7;500 ft. and went as low as 7;100 feet as I recall. I called out the altitude and asked the Captain why the VNAV had been turned off. At that same time; Approach advised us of a low altitude alert and we were told to climb to 7;500 ft. We climbed back up to 7;500 ft. and completed the approach with no other issues. At no time did ATC advise us of a pilot deviation and never asked us to call a phone number. When flying RNAV approaches; our company procedure is to make sure all crossing restrictions are entered into the FMS and checked. If an altitude does not meet the crossing restriction; we enter the crossing restriction altitude for each assigned fix. Then we put the final approach fix altitude in the altitude preselect and use the VNAV button to descend and meet all crossing restrictions; while monitoring the pink altitude in the top right hand corner of the PFD to make sure the airplane knows what altitude to descend to. This was an RNAV approach to LNAV/VNAV minimums; so we would select Approach mode after the airplane was within 30 degrees of the Final Approach Course and established inbound for the approach. We followed this procedure for this approach; however; somehow the VNAV button got disengaged which led to the airplane descending below our crossing altitude of 7;500 ft. at the VOR. The problem was compounded when I diverted my attention to the FMS and was not watching the Captain's autopilot selections and monitoring our altitude. Cause: VNAV function was somehow disengaged and we descended toward the altitude selected in the altitude pre-select. Weather in the area. Heavy rain shafts all around the airport and we were discussing whether to continue or request vectors away. I was programming the FMS and did not see the Captain descend below our altitude or press the VNAV button to disengage it. We were in IMC; but published missed would have put us into rain shafts; so we were discussing alternate missed approach procedures and relayed that request to ATC. We have also had some confusion about accepting the RNAV XX from the VOR; ZZZZZ straight in or just ZZZZZ straight in and have been given an altitude of 7;500 ft. to maintain; instead of 8;100 ft. like on the chart. Our pilots and other pilots are confused if 7;500 ft. is legal or if we would need to cross at 8;100 ft. like stated on the chart. I looked up and noticed the altitude deviation and called it out to the Captain immediately. ATC also advised us of a low altitude alert and told us to climb to 7;500 ft; which we complied with.