Air carrier pilot reported receiving a false terrain alert that resulted in an unstable approach and descent below PAPI glide path.

Narrative

On departure from ZZZ CA (Captain) noticed that the RA was showing 0 ft. We were on a cruise altitude of 12000 ft; as soon as we started to descend; the gear horn started to warn that the gear was not down. Disregarded that warning because it was due to the RA. We were cleared for the approach for visual XXL; backed up by ILS. FO (First Officer) turned into green needles 18 miles from ZZZ1 [Airport] and armed APPR mode. Soon the FMA showed the green 'GS' mode captured. Soon Captain and FO noticed that the autopilot was not descending for us. Canceled AP (Autopilot) and GS was already 1.5 dots going down. The airspeed was 180kts with flaps 20; FO called gear down. After the gear; FO tried to put flaps 30 and therefore almost leveled off for the airspeed to reach below 180 (we were nose down to follow the GS so airspeed didn't slow down much). During this attempt; GPWS false alarm started; yelling at us 'Terrain Terrain; Pull Up'; 'Too Low; Terrain'; 'Glide Slope' and 'Sink rate'. Captain called out disregard; it was clear that there was no terrain; but FO got distracted with the aural and started to lose cross-check. The warnings have continued all the way down to the landing; therefore distracting us from normal sequence and ATC calls. After the flaps 30 configuration was established; FO started to follow down the GS; but the lateral side was off the centerline. At some point we had PAPI showing 3~4 red lights; and Captain called out 'You're Low'. Passing ZZZZZ; at 6800 ft FO called Flaps 45; before landing check. FO called 'One Thousand' at 6100 ft. At this time; we were already in an unstable condition but continued. Soon after FO got even more unstable again showing 4 Red lights; Captain called 'my controls'. After the Captain took control we were established again with 2 white 2 red. Around 300 AFE the aural warning said something other than usual; 'Too low; Flaps'. FO noticed that the flaps were at 30 configuration; and called 'Flaps 45?'. It was unstable but FO did not call 'Go around'; CA put flaps 45 and landed.Lack of hand-flying skills. Distraction management. Confidence to call go around. Maybe muting the aurals might have helped; but also on the other hand aural did let us know that we were in flaps 30. I think it would've been better if I was trained as: If 'Too Low; Flaps' is heard; the next callout is 'Go around'. Just like an automatic call out like 'Go around thrust flaps 8' being automatic if I hear 'Missed Approach'. The first thing I heard 'Too Low; Flaps'; my instinct thought was 'Okay; we're low and flaps 30... so put flaps 45?'