Either you need to install a separate geyser feeding that bathroom or you need to increase the size of piping used from the existing geyser to the bathroom
Yes, if you're talking about a water softener, you can use copper piping.
The most thermal geyser area of Yellowstone is called the Upper Geyser Basin, which is home to the famous Old Faithful geyser along with numerous other geothermal features.
If referring to gas piping, NFPA prohibits this.
There are a number of factors that determine where the plumbing contractor decides to install it. If it is a gas heater, it needs to be located where it can be vented to the outside. Typically the heater should be as centrally located as possible to facilitate hot water getting to all of the fixtures it is attached to. They will attempt to minimize the length of the piping runs. Takes less piping and less work to install.
If you are looking for PVC piping try finding PVC Piping at several home improvement stores. Lowes Department Store is one such store that stocks PVC.
A hot spring that naturally shoots steam and boiling water is called a geyser.
Castle Geyser is a specific geyser located in Yellowstone National Park. It is a type of cone geyser, named for the cone structure that surrounds the vent where the water erupts.
A Conical Geyser (or cone)
$1200 to $1500 depending on the length of run
The process of copper re-piping is basically replacing all iron piping in a home with that of copper piping. Unless a homeowner knows how to do plumbing applications, a professional plumber should be hired.
Basement, if any, will oft times have PVC piping used for drain lines in it, if codes allow PVC piping.