A321 pilot reported unstabilized approach.

Narrative

Night flight. Originally FO (First Officer) leg; switched to CA (Captain) arrival for CAT 3. Cat 3 ILS Runway XXR ZZZ; wet; greater than 6000 RVR. Assigned 210 4000 on downwind. 190 speed on base down to 3000. Intercept 3000 and 170 speed to FAF. This would keep us too high. CA told FO to let them know that we would would be too high and it likely wouldn't work out. Mentioned it twice; no calls to ATC were made to relay this. Got busy fast. Put In 1700 ft and 1000 fpm descent. Was too tight and fast and high. CA made the poor decision to continue to 1000 and then plan to likely go around. Verbalized this. At 1000 ft the plane tried to capture the glide slope. This caused an erratic aircraft behavior leading to turning off the AP and auto thrust. Attempted to stabilize before initiating GA. This went badly and we got nose down. CA and FO said GA around. TOGA was not set. Correct attitude not set. The thrust did not react as expected. CA was confused. We were fully configured for flaps full landing. We then got a PULL UP. FO repeated pull up.CA executed very slowly and incorrectly into a GA and attempted to continue to stabilize the aircraft in the climb out. FO got flaps to 1. Oversped flap 1. FO seemed confused. CA set flaps to zero to stop the overspeed. Attempted twice unsuccessfully to re engage automation. Once level at 4000; automation was successfully re engaged. Continue around to another CAT 3 ILS XXR. FO set up and checked but approach phase was not activated. On final when CA pushed speed; plane sped up; CA pulled speed and called for activate approach. FO no response. CA activated approach phase; checked all criteria; stable except speed. Crew discussed continuing and we continued. Speed came down and on speed by 600. Successful auto land and taxi in. Med Auto Brake. AP off at 50 kts. Taxi in to Gate XX then broken jetbridge required tow to XY. Crew discussed event. Neither CA nor FO knew what happened initially at 1000 ft. CA took responsibility for the subsequent events and told FO that CA would file required reports. CA put flap overspeed in logbook and met with Maintenance.FO has 6 months in the 320; CA has 7. Trip started early am day 1; ended after midnight day 2. A circadian issue that the CA discussed at home prior to the trip.Both pilots have [several] kids.CA has dying family member adding life stress [to] manage the hospice care daily.