I have recently purchased a home with a Steamist steam shower -- no instructions for operation were available. Do you know where I can find owners manual/instructions? Thanks

Dismantling to discover the fault should be fairly straightforward to anyone with handyman skills.

Picture isn't very clear but I am guessing there has been a small water leak causing one of the heating element terminal posts to corrode through.
It would be a good idea, before starting, to contact the manufacturer or dealer to discover the price and availability of the parts that could be needed - element, seals, gaskets...

https://steamist.com/wp-content/uploads/bsk-pdf-manager/2018/06/TSC_Error_Codes.pdf

List of error codes

Orange discoloration is most often caused by rust or other minerals in the water.
Usually, the solution is to have a filter (or more than one) installed in the circuit.
God bless your efforts.

There are three things that affect this:
1. Incoming water temp.
2. Incoming water volume.
3.Temp of the device.
There are some other minute things like humitidty and altitude too.

PROBABLY TIE INTO A GFI CIRCUIT SEEING IT IS IN A BATH AREA

Contact Steamist directly for manual, DIY troubleshoot, warranty, etc:
http://www.steamist.com/contact.htm

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The heating elements had burned up in the unit therefor creating a dead short on that circuit. Main breakers on homes and buildings are VERY sensitive and will sometimes trip before the smaller branch cicuit breakers will . So the popping you heard was the heating elements breaking down inside the unit it can be some what noisy.

That is a main problem with the analog systems. Just not reliable as the new digital systems. To my best knowledge there is only one manufacturer making the 100% digital steam generators.