Air carrier First Officer reported Captain failure to maintain stable control of aircraft on approach and go-around resulted in momentary losses of aircraft control. First Officer stated captain failed to communicate; maintain proper speeds leading to pilot induced oscillations; exceeded bank angle and overshot altitude.

Narrative

WX prior to the approach: Vis 5000RVR. 400 OVC.RNAV GPS 2 ZZZ. I was the PM in the right seat. Captain was pilot handling. We were cleared by Approach; direct ZZZZZ cross ZZZZZ at or above 2000. Prior to ZZZZZ we were configured at flaps 5. A point past ZZZZZ we were told to contact the tower. I contacted the tower; we received the landing clearance. The captain then asked me to call them back and ask for the Vis (prior to FAF). 5000 RVR was the response. Captain then asked me to call tower back and request the ceilings (all between ZZZZZ and ZZZZZ1). The tower came back with 300'. The captain said 'we are not going to get in' (twice). I said; 'what are your intentions?' I then noticed we were approaching ZZZZZ1 rapidly. 'I then said; we are nearly at ZZZZZ1 and we are not fully configured'. Captain asked for gear down and flaps 15. As I put the gear down I said were are passed ZZZZZ1 and you are not configured for landing. Captain then said; 'go around Flaps 15'. I said; 'you're at Flaps 5'. Captain called for flaps 15 again. I said 'you're at flaps 5'. I called 'positive rate' he called gear up. Captain again asked for flaps 15. Again I said you're at flaps 5. I then noticed our pitch was at 22 degrees we were decelerating through 170 knots. The slowest speed I saw was 167 knots with the low speed amber indications in full view and a trend vector decelerating. I called pitch and speed. Pitch down pitch down. During this oscillation I also noticed the aircraft symbol was high above the pitch bar and well to the right of the roll bar. The captain then pitched to the horizon and we started to accelerate. I said follow the command bars. There were PIO (Pilot-Induced Oscillations) in pitch and roll. The Captain began a roll to follow the roll bar command for the missed approach procedure; but rolled in excess of 40 degrees. We received a 'bank angle warning'. I told the captain to roll the wings level. Then follow the flight direct. I was also told to contact approach. We were rapidly approaching 2000 ft and said as much to the Captain; we rocketed up through 2000 ft. I said to the captain I need you at 2000 ft. He stopped the climb at 2500 ft. Descended to I think 2300 ft. Again I said I need you at 2000 ft. I was also trying to sound coherent with ATC. I requested 3000; as the captain was not descending back to 2000. Again we got into a pilot induced oscillation. Again I was trying to get the Captain to follow the command bars. He seemed to be struggling with following the command bars. We stopped the climb at 3500 ft. At some point I noticed the A/T (autothrottles) were disconnected. I reestablished the a/t gave the captain 200 knots. He descended back to 3000 ft. During all this the captain on numerous occasions kept apologizing. There were definitely G loadings both negative and positive during this event.I remember seeing as much as 3600 FPM climb down to 1200 FPM descents. Roll in excess of 40 degrees.