I have met a lot of those intercoms, and while the door release is AC powered ( or DC powered if you put in the optional battery back up unit, which keeps the entire system running with power loss for a few hours) the actual door contact really needs to be either a dry relay contact, or an optocoupler with darlington output, which is not exactly stellar speed wise, but which will operate with 1mA of LED drive no problem. 4N32 or 4N33 is cheap and will work, just connect emitter to 0v and collector to LZ, as the door interface unit operates that section using all DC, so as to reduce hum on the long internal wiring.
Power wise you cannot draw any power from anything, as the ring actually is a tone used to operate the handset speaker as sounder, so it has only a 2 or 3 tone AC signal, driving a 30R speaker and is generated by a pair of CMOS hex inverters in the head unit, so has only limited power capacity. You either need to have a local battery, either lithium or primary cell, or a local DC supply from say a old phone charger.