Hi,
1) Yes, for your purpose here.
2) Unregulated DC would be e.g. a steady-ish 5V that goes from e.g. 4.9V to 5.1V, what you see and use as the input voltage to the voltage regulator after the bridge rectifier and smoothing capacitors you called diode ring, etc.
Read about how to calculate smoothing, or bulk, or filtering, capacitance in power supplies, it will help, and that in voltage regulator datasheets there is a useful to know parameter called line rejection - how much input ripple a regulator can handle and with regard to frequency before it can't keep up any more and regulate the output.
I'm sure you know that Zener + BJT regulators are fossilized circuits and (very) bad due to various weaknesses Zener and BJT each have, plus lack of real Error Amplifier feedback, but useful as introductory learning concepts and tools. Have fun!