Air Carrier First Officer reported they initiated a go around when ATC issued vectors to final too close to the airport resulting in a low speed warning and unstable approach. During the subsequent approach the Captain descended below glidepath resulting in a Low Altitude Alert from ATC but were able to recover and land.

Narrative

We were being vectored for a visual approach to Runway XX at ZZZ The weather was VMC with good visibility and winds were out of the west at approximately 15 knts. I was the Pilot Monitoring and the Captain (CA) was the Pilot Flying. The last vector required a bit of a tight turn to final. We were configured flaps 2; 170 kts. and the gear down turning to final; with the approach armed and all automation engaged. During the turn; the CA managed speed and we continued with the flap configuration. About halfway through the turn; I noticed the hook rising and the autothrust was slow to spool. We got the 'SPEED SPEED' aural alert. At this time; the CA disconnected the autopilot and we performed a soft go-around. I informed ATC that we were going around because we were going to be a little high. ATC provided us vectors for another approach. Since we were above 1000 ft. we elected to remain configured to for the vectors for another final. On the base turn; we were pretty close to ZZZZZ. The CA started a descent to 1500 ft. I stated that the altitude at ZZZ was 1900 ft. At about 1700 ft.; ATC stated that they had a low altitude alert. We started the climb back up and intercepted the glide path. At 1000 ft.; the CA decided the automation wasn't providing satisfactory performance so he disconnected the autopilot and autothrust and continued the approach by hand flying. All checklists were complete. I verified all paramaters were stable at 500 ft. and we continued the landing. I believe that the tight turn to final and shorter than normal vectors contributed to the low speed event. The event very likely would have been prevented by requesting a longer downwind/base turn on the final approach. Worthy of note; I was surprised at how slowly the autothrust was responding to the demand. In X years and 3;700 hours on the airplane; I hadn't experienced that much of a 'lag.' That said; I fully acknowledge that we didn't help ourselves in anyway accepting short vectors. There was certainly some startle factor as well. I should have been more assertive with the CA and ATC in requesting a longer final. We were a heavy; it was a little windy; and the traffic in the area was light at the time. In the past; I have asked for longer finals if I felt that the vectors were going to be tight for the aircraft performance and configuration. I'm honestly not sure why I didn't this time. I know better. Going forward; I will be much more assertive with the crew and ATC if I see potential for a similar scenario developing. I see no reason to ever accept a vector that close to the FAF.