A321 First Officer reported receiving multiple ECAMS for the number one engine during cruise. The flight crew performed an in-flight shutdown of the affected engine and continued to the destination airport.

Narrative

At cruise; FL330; aircraft began to vibrate; ECAM presented ENG 1 STALL. Ensured Captain remained pilot flying (PF) by stating 'Your Aircraft' and ran the Quick Reference Checklist. As I was running the Quick Reference Checklist the ECAM went away and the vibration subsided. We monitored engine parameters for abnormalities and found that the #1 Engine had a higher EGT than the #2 Engine but still in the green (normal limits). We (PF and (PM) pilot monitoring) began reviewing QRH material and potential diversion airports in the event the engine continued to have issues. We came up with a plan for enroute diversion if needed; and briefed what we should do if the engine failed on descent or on approach. Planned a Flaps 3 approach; reviewed Single Engine go-around and 10-7 requirements. The engine continued to run at about 30-60 degrees hotter than the #2 Engine; but still well within normal ops limits. No further vibrations at altitude. No issues during descent. I monitored and continued to write down EGT for both engines on descent (and presented to [contract maintenance]). Turning final at about 2;000-2;500 ft. MSL the #1 Engine began to vibrate slightly; as the gear was lowered and Flaps 3 was initiated the engine began to vibrate substantially; spitting and sputtering. I announced to the Captain (PF) that Engine #1 was failing based on the reduction in power and higher EGT. An ECAM appeared stating ENG 1 STALL. As we were about 3-4 miles from landing and immediately after ECAM I ensured Captain had the aircraft; reviewed the QRC; as the ECAM went away again PF pulled #1 thrust lever back as I guarded #2 thrust lever. I ensured Captain placed #2 thrust lever in maximum continuous thrust. We decided to continue on a Single Engine approach and landing after a very brief discussion (as we had already briefed this earlier in flight if the engine were to fail on final). I requested priority handling to ZZZ; stated nature of the situation (southeast landing; engine failure; Souls on Board; Fuel on board) and that we would taxi clear. The Captain (PF) landed uneventfully as the #1 Engine had remained in operating limits after reducing power. Upon landing I started the APU. As we taxied clear of the runway the Tower controller stated that the #1 Engine was on fire and that she saw flames coming out the back as well as smoke. We just then received an ECAM stating the ENG 1 OIL FILTER CLOGGED. The Captain immediately shut the #1 Engine down. I asked the Captain if he wanted to consider the evacuation checklist; but then The Tower Controller stated the flames had dissipated but there was a great deal of smoke still coming from the engine exhaust. Then the Tower Controller stated the smoke was subsiding. We did not attempt to run the evacuation checklist because the flames/smoke situation appeared under control. We had already stopped on the ramp area clear of other aircraft; and as the ARFF (Airport Rescue and Firefighting) trucks approached we attempted to gain comms with the trucks. We could not get the same frequency as the ARFF trucks and relayed information through the Tower Controller and attempted hand signals with the ARFF crew. The ARFF crews stopped approximately 30 yards from the front of the aircraft and approached without equipment as it appeared the fire had gone out. There were no indications of fire from inside the cockpit. After ARFF inspection we taxied to the hardstand area for further inspection before allowing passengers to deplane via air-stairs. It would have been nice to have the ARFF frequency available to communicate directly with ARFF as they approached rather than relaying through Tower frequency. Language barriers are often an issue in foreign countries but did not play a significant factor during this event. However; I am unsure if the Tower Controller actually knew what 'PAN PAN' meant.