Air carrier pilot reported descent below glidepath and flight toward terrain during approach. Flight crew corrected and continued to landing.

Narrative

I called for go around at around 200 ft msl due to being Vtarget + 15 to 20 and far right of centerline. During the go around the airspeed went no higher than 249 knots with flaps in transit from 5 to 1 position. I assumed control to finish recovery. The exceedance lasted less than 5 seconds as recovery from the anticipated overspeed had already been initiated prior to the actual exceedance. Finished recovery; completed after takeoff checklist; then initiated approach checklist followed by a reconfiguration for another approach. Transferred control back to the First Officer.During the second attempt for RNAV XX; the airplane was configured with all appropriate modes selected. My eyes were outside as we were vmc. Passing the final approach fix; the airplane initiated the descent to the set minimums. I noticed quickly the airplane was descending faster than it should be according to the papi. When I looked back inside vnav speed never switched to vnav path. At 3 red; 1 white on the papi I assumed control again; disengaged the autopilot and auto throttles; arrested the descent rate and leveled to regain 2 red and 2 white on the papi. This all happened very quickly; but recovery was successful and continued to landing without further incident.During both of these incidences; everything happened very quickly. I'm trying to remember all I can; but in the moment I just remember not liking what I saw altogether and taking action immediately to fix it. The overspeed was entered into the records after block in.I've done the RNAV XX in ZZZ several times and don't remember having any trouble at all. This time there was a combination of automation issues and approach stability; which I ultimately believe came from the automation issues or unexpected guidance. These events were all unexpected to me. Everything was ok and appropriate until all of the sudden it wasn't and corrections were necessary. Memory of these two events indicate the problems arose very quickly and without any noticeable trend to unfavorable conditions until all of the sudden the total picture of information was unfavorable. I believe as a crew we reacted appropriately to these unexpected conditions. Therefore; I'm not sure what else was to be done.