Howdy - you can do all these things if the protocols used with the apartment gate and work door are the same as those used by the ring. This isn't always possible as some versions of wireless card use different frequencies for communication, and so you're going to have to look into it a little yourself.
As things stand, you can get a compatible apartment door lock and you can unlock your phone with the 2016 ring which doesn't do payments. At the moment I'm not able to say whether the new payment ring will allow these things because I haven't had one for testing.
Perhaps @johnyma22 can weigh in on this.
I don't think that you'll be able to use the new payment ring for the gate or the work door, but I could be completely wrong on this.