Air carrier pilot reported temporary loss of aircraft control due to wind shear on final approach. Flight crew performed a go-around and landed.

Narrative

While riding in a jump seat of an air carrier I observed and had to alert the crew to a developing situation that could possibly have led to an undesirable aircraft state. While on approach around 800-900ft AGL I heard an audible 'wind shear;' the PF responded by increasing power and climbing. After leveling off at 200ft above our assigned altitude the crew attempted to clean up the aircraft; the PF said 'let's clean it up.' At this time the gear was brought up and multiple audible 'landing gear;' alerts due to the flaps still being in landing configuration. We got our first flap over speed at this time; the PF was still hand flying with auto throttles off; very little communication between PF and PM on aircraft configuration and selected modes. ATC attempted to give us a left turn twice and a climb to a higher altitude but PF was struggling with hand flying the AC. The PF started a descent and a turn to the right; as the speed increased the throttles were brought to idle or near it. We got a low altitude alert from ATC to which the PF responding by shallowing the descent. I noticed the speed moving towards the redline on the bottom of the speed tape and I got on the intercom and said 'watch your speed; you're getting slow and still descending.' The PF responded by starting a gradual climb and adding power; there still was no automation engaged and soon got another flap over speed. Eventually the airplane was cleaned up and automation was re engaged. Checklists were completed and a second approach was accomplished to a landing. After parking at the gate I asked the crew if I could debrief what I saw and they were both very open and receptive. Although I have never flown that aircraft or at that particular airline I was a LCP (Line Check Pilot) at my previous airline and felt I could give them some advice on how to handle a situation like that in the future.