Electronic – Why are transformers unregulated

The 820 ohm is almost certainly for current limiting.

Without knowing more about the circuit it powers it's hard to be exact about the 27k, however, I think it may be to present a minimum load to the secondary to limit light or no load voltage (possibly to discharge any filter caps also and/or related to PMOS turn on battery/AC switch circuit to pull gate back to ground)
This is often used if the following circuit has no proper regulation (i.e. linear or switch mode)

The cores in the transformers do not behave linearly. In general you can use less than the specified voltage, but not (much) more. If you connected a 120VAC transformer to 230VAC you would get smoke because the transformer core would saturate, the effective inductance would be less, and the current would be limited only by the copper resistance in the winding. This is actually a useful 'feature' since the flux is limited by saturation the output voltage is also limited and the transformer will greatly attenuate large spikes on the primary.

If you use a 230VAC transformer on 120VAC and stick to the rated output current you'll have no problems with smoke, however the transformer will be heavier and more costly than the cost-optimized design (it will likely also be a bit more efficient than the cost-optimized design).

Putting transformer primaries in series (unlike secondaries) is not a great idea. It may work in some circumstances, though the tendency will be for one transformer to run warmer than normal, so I would not recommend it in general.