Air carrier B737 First Officer reported an unstable approach during a night visual approach after the Captain overshot the turn to final. The First Officer had concerns about fuel remaining and after correcting for the ATC issued low altitude alert; the crew landed.

Narrative

After the ZZZZZ Arrival; we were cleared for the visual to Runway XXL at ZZZ. The Approach Controller gave us a base turn and asked us to call the field in sight. The Captain called the field in sight and began the base turn and disengaged the autopilot. It was a tight base turn; ultimately inside of ZZZZZ1. Once the PF (Pilot Flying) began the turn; we also began the final configuration changes; switched to Tower; and completed the Before Landing Checklist.During the turn to final; I could tell the we were turning tight based on the navigation display. However; my primary attention was on the configuration; radio calls; and checklist. Sitting on the outside of the turn; I trusted that the PF had the field in sight. I considered that there might be a misidentification; but since we were on the left runway and the turn kept us away from [Runway] XXR; I dismissed the idea. After all the tasks were complete; we were left of centerline with a correction. The PF admitted to 'biting off' on the wrong set of lights. I suggested turning more right; which the PF did; around 1000 ft. Before 500 ft.; Tower issued a Low Altitude Alert. In retrospect; this should have triggered a go-around; especially on a visual at night. At the time; I estimated that the PF's correction was sufficient and that we would make the 500 ft. gate. Visually; we also seemed to be close to glide path; so I thought the altitude alert might have been based more on our lateral path than our vertical path. Identification of the vertical path was complicated during the correction to centerline by conflicting information. The PAPI showed us below path while the ILS showed us above. I was aware that both may be limited to a particular envelope left/right of course and might not be correct until closer to centerline. I made a comment to the PF about not trusting the PAPI yet. However; the visual glidepath indications were probably the more accurate. By 500 ft.; we were essentially wings level and on profile and continued the approach.We were also low on fuel. Our planned landing fuel was 4.7 based on the load of 8.2 in ZZZ1. On the arrival; the last number I remember on the Prog page was 4.3. This meant that a go-around would immediately put us into a minimum fuel situation. I didn't have time to do all the math at the time; but I was concerned at the time about running out of options. However; assuming 1.5 for a missed approach and landing; we could have landed with about 3.5 and stayed above the FAR Reserve listed on the Release. I don't have minimal experience managing low fuel states and we probably would have been okay with 3.5; considering the clear weather and nearby airports. Planning a landing fuel that doesn't allow for a go-around without the Fuel Low lights illuminating is a poor plan. However; I hinted and hoped at the situation in ZZZ1 rather than asking directly for more gas.I should have called a go-around for an unstable approach below 1000 ft. due to both the lateral and vertical deviations. Deviations in the lateral path made deviations in the vertical path hard to measure. In the future; if I can't positively determine that we're stable; then we are unstable. A slightly longer final would provide a little more time to deal with the turn before managing the descent and allow a lower rate of descent from the radar altitude to catch the glidepath. It also allows more time to correct the lateral path before reaching 1000 ft. in the event an error occurs. Also; I will insist on enough fuel to do a go-around and land by 4.0 in order to remove the perceived fuel pressure.