G-IV pilot reported a fuel leak during departure climb. Flight crew returned and landed uneventfully and the aircraft was removed from service.

Narrative

The morning of the Day 0; with the passengers boarded; we started engines to taxi to XXR. After 10 minutes of waiting for taxi instructions; I asked the Tower how much longer for taxi. They said it will be a few minutes as there was a line of departures at the end of XXR waiting for takeoff. I shut the left engine down to conserve fuel as we were going to ZZZZ on a 4-hour flight. About 5 min later; we were given taxi instructions. I started the left engine and performed all the checklists. We took off from ZZZ; and about 5 minutes later; one of the passengers yelled; 'There is liquid coming out of the wing'. As we were above 10;000 ft; I went back to see what he was looking out. As I looked out the window; I saw a stream of mist that looked like it was coming from the right wing over the wing fuel cap. The sun was bright; and the trail of the fuel mist was directly behind the fuel cap. I immediately decided to return to ZZZ. I told ATC that I needed to return to the airport as we had a fuel leak and that I was NOT [requesting priority handling]. We were given instructions to make heading turns to be put on the ZZZZZ 5 arrival. During the return to ZZZ; the passenger said that the fuel leak stopped and that the stream behind the wing was not there anymore. I continued to ZZZ. Coming into ZZZ; we were at around 4000 feet and about 4 miles from the field. the Approach Controller was busy dealing with a Cessna 152 not being able to make the runway and didn't clear us for the approach until we were 4 miles out. He cleared us for the approach; switched us to Tower; and I had to perform a right 360-degree turn to be able to make a more stable approach to land on the runway. I did not want to perform a go-around due to the fact we had a fuel leak. We landed without incident and taxi to the FBO. Our Director of Maintenance (DOM) was there; and I explained what happened to him. He removed the overwing fuel cap and cleaned the gasket. Later; he told me the fuel was coming out of the lower fuel vent; and that is what we all saw. He cleaned the lower part of the wing. Then the aircraft was returned to service by the DOM.Before the next flight; the First Officers DU (Display Unit) 3 display was showing a 'X' on the screen; and we had a #3 symbol GEN fail; CAS message indicator. I moved the symbol GEN switch to the alternate position; and the First Officers screen came back to normal. Person A; our Mechanic; pulled the circuit breaker to get it to reset; which did not work. Then we performed an aircraft hard shutdown for 10 minutes. After 10 minutes; we started the APU and initialized all the systems. The CAS message was still on the screen. We moved the switch to the alternate position; and again the DU screen came back to normal. Since it was able to me MEL'd; it was written up by the DOM and MEL'd. I added 500 gallons of fuel. To complete the trip.We started engines and proceeded to XXR for takeoff. After takeoff; about 5 minutes after departure; the fuel stream started again; and the passenger once again informed us about it. I sent the First Officer back to inspect it and he took a picture of it. While he was in the back inspecting the fuel leak; I informed ATC again that we needed to return to the field for a fuel leak. I told them I was not [requesting priority handling]; but I had a small fuel leak and needed to return to the field. We were given instructions to intercept an RNAV course; and I noticed that when on heading and the RNAV armed; it did not intercept the course. I lost my NAV information on DU 2; but I still had a indication on DU 1. I told ATC that I lost my navigation systems; but I could still do headings and vectors. The First Officer returned to his seat; and I informed him of what was happening with the navigation systems. ATC gave us a heading of 210 degrees; which we followed. About 2 min later; ATC asked us what heading we were on; and I told them a 210-degree heading. They replied that we were tracking about245 degrees across the ground. The passengers again told us the fuel leak had stopped; but I continued to the airport to land. It was VFR conditions; and I told them I had the airport in sight and I could dead reckon to the field. We were cleared for the visual approach for XXR in ZZZ. I slowed down and put the aircraft in a fully configured for landing about 7 miles out from the airport. We landed without incident; and when we taxi'd off the runway; I noticed that the airport firetrucks were coming toward us. They performed a visual inspection as we taxied by them; and they said nothing was coming out of the wings. We kept going to FBO ramp and shut down the aircraft and debarked the passengers. I talked to the Fire Chief and told him what was happening; and also airport operations. Our Maintenance was still there; and they said the airplane is grounded now; and they would write the discrepancies up.