I think personal responsibilities of a diver are to be able to plan their dive as if they we're diving solo, but relegating their redundancy in their buddy rather than equipment. This would mean knowing your dive plan, air plan, plan of navigation, hazards etc.
In addition they should have a plan of buddy separation and even basic buddy rescue; getting an unconscious buddy to the surface without putting anymore danger into themselves.
As for the DM's responsibility, ideally that person should be a safety line in case of an inexperienced mistake, but should not be relied upon. The DM should give their experienced input on the dive site and dive plan, but ultimately it falls upon the divers to create their plan, dive their plan, and the DM is there to correct any inexperience mistakes, because he/she is the experienced person on that site. Ideally at least, it sometimes doesn't come out that way.
In addition they should have a plan of buddy separation and even basic buddy rescue; getting an unconscious buddy to the surface without putting anymore danger into themselves.
As for the DM's responsibility, ideally that person should be a safety line in case of an inexperienced mistake, but should not be relied upon. The DM should give their experienced input on the dive site and dive plan, but ultimately it falls upon the divers to create their plan, dive their plan, and the DM is there to correct any inexperience mistakes, because he/she is the experienced person on that site. Ideally at least, it sometimes doesn't come out that way.