Probe 100 Ohm pipe mount with connection head (PTD-1)

No, as long as it's properly installed. However, improper installation, use, and/or maintenance of electrical heating cable can cause fires, electric shock, and/ or frozen pipes.

Yes, it can be used for both application types to prevent pipes from freezing and bursting during cold weather.

Heat trace, heat tape, or heating cable for pipes is typically an electric heating cable that can be attached to the pipe which helps keep non-flowing water pipes in poorly insulated perimeter walls flowing despite harsh winter temperatures.

Unfortunately there's no set answer for this because it depends on many factors such as the diameter of the pipes, the installation density of the heating cables, the outdoor temperature, the installation of thermal insulation sleeves, etc.

There are too many variables to provide an accurate answer. Even though this product is designed to keep pipes from freezing, it is not designed to thaw pipes. If your pipe has frozen with the heat tape installed and energized, please check the placement of the built-in thermostat and verify that the insulation has been properly installed and waterproofed.

By attaching a heating cable to the exterior of a pipe, it will transfer the heat to the pipe to prevent frozen pipes. And with the use of pipe insulation the heat will be evenly spread and won't dissipate as quickly.

No.  It is not listed for this application, and it is not warrantied for use in direct burial or wet applications.