Air carrier flight crew reported a critical ground conflict during taxi out from ramp. The First Officer transmitted 'STOP' command to the other aircraft and avoided a collision.

Narrative

During taxi in on previous flight the flight crew noted night ramp controller training appeared to be taking place. At Gate XX; terminal ramp illumination lights ruined our night vision. During the next flight; at pushback; the tug driver stopped suddenly and started and stopped again. When I inquired as to what was happening; he stated ' we cannot be sure if we are clear of the aircraft behind us and what his intentions are'. As the pushback resumed; we witnessed a dark airplane being pulled by a super tug off our left and the clearances looked very close. We did not observe a beacon on the airplane; tug caution lights; or hear any transmissions from this aircraft or ramp tower concerning this aircraft. After the tug driver disconnected; we were cleared to taxi to the top of the alley; then recreated to [taxiway]. As we turned towards [taxiway]; we were directed to stop again and another aircraft was cleared in on our left where the passing space was not evident. As the First Officer (FO) and I observed this aircraft from right to left begin his left turn; we realized a collision was probably imminent. Quick words were exchanged and the FO transmitted on the ramp frequency 'STOP; STOP; STOP!'. The aircraft stopped; allowing us to make a right turn away from the danger of collision and proceed.Night; weather; visibility; ramp does not appear as well lit as XY ramp side; night vision from XY [ramp] ruined for pilots and ramp personnel; controller training in progress; on a weekend; during high work volume on the ramp; ground markings and protected passing areas unclear; non standard RAMP TOWER phraseology; super tug driver communications for SA of all involved. Either of these back to back events in less than 10 minutes had the propensity for aircraft to aircraft damage. Kudos to an alert ground crew man and to the FO for stopping each collision event. As a result of these 2 events both cockpit crew members experienced an adrenaline dump during and after the flight which affected us both differently.Use certified controllers on all ramp areas in ZZZ; change ground markings; have charts give accurate depictions for use with standard phraseology; better lighting for XY and XX ramp areas; Super Tug driver communications; lighting on aircraft and tow vehicles