A new water heater was installed when I bought the house a year ago and is also well water. The hot water smells like rotten eggs and is full of gray particles that float and turn the water very dark and stain dishes, the tub, etc. The water heater has always been set at 120 degrees and the well was free of bacteria when I moved in. Could the tank just need to be drained or is it something else?

The rotten egg smell is Hydrogen sulfide gas. This is not an uncommon smell in water, especially in some areas of the country. If it is a recently occurring thing in an established well, I would expect the present of bacteria that produce the gas. A new well, may need some method of removing it from the water.

Here is a website, one of many, discussing the topic. http://www.water-research.net/sulfate.htm

Hope this helps with an answer, and best wishes.

When was the last time that you flushed your water heater, you need to flush it frequently I do mine every 2-3 months some experts suggest every month, in your case lets flush your water heater first and see if the smell is gone, next step would be to check the water heater Anode rod see the images, Thanks.

John

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