Cessna 208 Caravan First Officer reported the Captain flew through the localized on approach; then entered a steep bank and lost altitude while turning to regain the localizer.

Narrative

My Captain and I were shooting the approach for [Runway] XX into ZZZ. He was the Pilot Flying; and I was the Pilot Monitoring. The Pilot Flying had the autopilot set up on the heading assigned by ATC to intercept the localizer; with the approach mode armed.As we approached closer to the localizer; we noticed that the autopilot was not turning to intercept. This began to make me concerned; due to the fact we were starting to go through the localizer if no adjustments were made. Acknowledging this; I verbally told the Captain to make a turn to the left in order to get back on the localizer.After multiple verbalizations; I received no verbal response or corrections from the Pilot Flying. This began to make me feel uneasy. We continued on the same heading with no correction for the localizer. ATC then came on to give us a heading to re-intercept the localizer. The Pilot Flying then corrected the heading with a 45 [to] 55 degree bank without maintaining altitude.This caused us to descend rapidly; about 500 [to] 700 fpm. Due to this; I began to feel unsafe and took control to apply back pressure in order to regain altitude. After making the correction; the Pilot Flying told me; 'I got it;' and remained on the controls for the duration of the flight. Due to the loss of altitude; we received another correction from ATC to climb to our assigned altitude and turn to the heading to get back on the ILS.After re-establishing on the ILS; we were able to continue the approach for landing. As we were taxiing on the ground; we were advised to copy a phone number for a possible pilot deviation. Once we were parked on the ground; the Captain called the phone number.