B747 flight crew reported receiving a Gear Tilt EICAS Message on take off. After confirming the fuel load was sufficient to continue to destination airport; the flight crew encountered fuel management issues on approach resulting in an engine flame out and roll back. The crew continued the approach and landed safely.

Narrative

After takeoff; when the Captain called positive rate; I commanded the landing gear up. As the Captain attempted to bring the gear lever up; it did not move to the up position. The Captain advised me that the GEAR TILT message showed on the EICAS with the respective aural warning. At this time he commanded to engage the Center Autopilot and to open the speed intervention window on the MCP; in order to limit the air speed to 250 kts. while the flaps were being retracted.As soon as the flaps were retracted and the speed was within the limits; I transferred controls to the Captain and he also advised me that he had communications. He then instructed me to get the QRH procedure for the GEAR TILT EICAS MSG procedure. The Captain advised ATC that he had a landing gear issue and requested to maintain FL 200; after I completed the QRH procedures. The gear could not be retracted; Captain instructed me to phone patch Operations so we could figure out the fuel and flight plan amendment to continue to destination per the QRH performance inflight. We collectively decided to continue to destination and we used the QRH performance at FL 250. After Operations calculated the amended flight plan and fuel burn from our current position (time remaining; 1 hour 27 minutes & a distance of 500 NM). The decision to continue was based mainly on the amount of fuel onboard (45;000 KG); at the time of the re dispatch calculated fuel remaining it was shown to be 18;000 KG at landing; giving us a fuel burn of 27;000 KG with all the gear extended. Once we got to top of climb; the fuel burn calculation was slightly different than planned.When we were on approach and beginning the approach with a left downwind leg to Runway XXR; we were instructed to change to Runway XXL due to an emergency aircraft ahead of us who were approaching Runway XXL. At this point and time; the first Alert comes on stating a Warning on Engine Number 4; then Engine Number 4 started to fluctuate. I then proceeded to make the proper corrections and called for Engine Number 4 flame out QRH procedure. Then; the fuel press on Engine Number 1 EICAS MSG comes on with an aural warning. ATC was giving instructions to all aircraft that there was a situation in progress and were told to hold all aircraft arriving. We informed the Tower that we were having an issue with an engine losing thrust. By recall I turned all fuel pumps on; the engine restarted but then shut down about a few minutes after. ATC gave us a vector to put us 15 miles behind the emergency aircraft ahead of us. When we started turning on final to intercept the localizer; the fuel press on Engine Number 4 EICAS MSG came on and the Engine shut down; we were at 1;500 ft.; we were approximately 15 miles out when this happened. At that point the Captain advised me that we are committed to put the aircraft on the ground safely. We requested priority handling right away. We tried to vacate the runway but couldn't because the steering system was inoperative. There was no time to run any checklists and under the Captain's authority he then decided (I concurred) to land. After we landed we spent approximately 45-55 minutes on the runway waiting for a tow truck to reposition us to the ramp.The QRH check list for gear tilt send us to check the inflight performance for gear down and never directed us to check the synoptic fuel page; just check the total fuel qty and fuel flow. Write in the QRH when there is a failure that degrades the aircraft performance open the synoptic page in order to obtain an accurate fuel reading.