It will be impossible to answer some of your questions accurately, based solely on the information that you provided. We don’t know exactly what you have or even what county you’re in.
Did the transformer fry?
It is a real possibility. Burning smell bad. But, we can’t be sure. Someone with expertise will be able to test the transformer with a multimeter and know if it is good or bad.
Is it common to be wired to the main?
No it is very uncommon. Absolutely nothing, except branch circuit breakers, should be wired to the main breaker. I would guess that you missed something, possibly a sub-panel. But, if the light and transformer are indeed directly connected to the main breaker, then someone has done a terrible (DIWHY) wiring job that would be illegal in many countries.
The Ring door bell requires a special resistor when being powered by an AC doorbell. This is discussed in the installation instructions. I’m guessing that this resistor was not in place when your friend did the installation. But, again I cannot know for sure.
My opinion is that your friend does not know enough about this to do the job. My opinion is that you should hire an electrician to:
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Identify the breaker you could not find.
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Test the transformer, and replace it if needed.
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Install the door bell correctly and determine if the Ring itself was fried in all of this misadventure.
The WT00Z is a basic Z-Wave scene control button that should work with any Z-Wave controller. Though I do not have experience with Vinit.
The WT00Z can only be reset by Z-Wave Exclude. It would be my guess that the WT00Z is not properly Excluded.
Put any Z-Wave controller in Exclude mode and tap the WT00Z. I don’t remember for sure, but a double tap may be necessary for the Include/Exclude on this device.
After successfully excluding the WT00Z, you will need to perform an Include with your Vinit controller.