P2012 First Officer reported during climbout they experienced a fuel pressure low indication resulting in inflight engine shut down and fuel leak and return to the departure airport where they landed safely.

Narrative

During climbout at approximately 5;800 feet; the right-hand engine RPM began fluctuating erratically; accompanied by the RH FUEL PRESS LO" CAS message. The aircraft was stabilized; and the climb was discontinued starting a drift down to 5;000 feet. Turned the RH FUEL PUMP from AUTO to ON; that had no effect on the low fuel pressure indication.Then the engine was operated at a reduced power setting; and a decision was made to return to ZZZ. The "RH ENG FUEL PRESS LOW" checklist was then called and completed. A few minutes later; a fuel-like ODOR was detected by the crew in the cabin; and a FUEL LEAK was observed from the bottom rear side of the same engine; Decided to DO the 'ENGINE FAILURE; FIRE; or SEVERE DAMAGE' memory items and requested assistance upon landing. The 'ENGINE SEVERE DAMAGE' checklist was then called for. Upon landing as coordinated with tower we the aircraft remained on the runway for a check due to a fuel leak observed by the first officer at the same time the odor was detected.We were assigned ILS XR for landing. ATC informed us of another aircraft experiencing smoke in the cockpit and inquired if we were comfortable landing second. Given the availability of multiple runways suitable for our performance; we agreed. Maintaining 5;000 feet at approximately 120 knots; we intercepted the ILS. Once visual confirmation was established; we followed the PAPI from around 700 feet to touchdown. Due to the ample landing distance available and low aircraft weight (with only one passenger on board); the Captain elected to use FLAPS TAKEOFF for landing. Upon touchdown; the remaining engine was shut down; allowing the firefighters to approach. We requested their assessment of the right-hand engine fuel leak; though the odor and apparent leak ceased after the engine was turned off.It was determined that it was safe to remain on board; and an evacuation was not necessary. We decided to stay onboard with our single passenger; whom we briefed shortly; explaining the situation: engine issues; a fuel leak; and the need to remain seated until cleared by the fire department. After clearance from the firefighters; They inquired if the passenger wished to disembark and ride in their truck. Following reassurance that it was safe to remain on board; the passenger opted to stay with us. The aircraft was towed back to the ramp; where we parked without any further issues.Cause: Mechanical issue."