F900 Captain reported critical hydraulic failure inflight resulted in a divert and landing completed after manual gear extension.

Narrative

Autopilot 1 + 2 failed on the ground during cockpit setup from ZZZ1. We attempted a full reboot of the aircraft; but the message remained. We contacted maintenance. We were able to provide relief from our MEL of Autopilot using: MEL ATA 22: Pg. No: 22-X/X-X Autopilot (AP) Function. We flew the trip in non RVSM at FL270. 'Hyd. 1; Pump 3' Amber CAS Message appeared about 40 minutes into the flight at FL270. We recognized that it was Pump 3. The number one system was unaffected; we pulled up the synoptic page; viewed and monitored; we ran the checklist: 'HYD 1 System operations will be longer. No further Pilot action required. Status page; checked.' We contacted Maintenance by phone; advised them of the Failed #3 Pump. We discussed that pressure and quantities remained full; all systems were Green; no loss of fluid; we would monitor the system and continue the flight to ZZZ2. Approximately 30 min after Hyd. Pump #3 failed; we lost all Pressure and Fluid in HYD #1. An Amber; 'HYD #1 Pump 1+3' CAS Message appeared and 'Hydraulic Low Level 1'; we immediately diverted to ZZZ; as it was the closest suitable airport for the appropriate runway and conditions. We ran all abnormal checklist/briefed all status notes on System 1; using manual gear extension and landed at ZZZ. We informed ATC on approach after a series of vectors; we may need a tug as we had Hydraulic issues; needed to run our checklist and lost our NWS (Nose Wheel Steering); however once on the ground we were able to use rudder and differential power to taxi to the FBO from Runway XX. Upon post flight; we noted Hydraulic Fluid covering the bottom of Engine #3 Cowling. Maintenance has been involved and Dassault Falcon Jet notified by our maintenance team to further look into the situation of what caused the Two Pumps to Fail and Loss of Hydraulic Fluid in System #1.