Unfortunately it is not.
This cable turns on at 38 degrees and turns off at 50 degrees
The thermostat is the black raised portion on the cable
For each foot, there is 7 watts
This cable is only recommended for pipes that are water filled at all times
If the downspout is aluminium you would have better success since it's more conductive. But you would have to insulate the heck out of it in winter.
I think it is intended to be placed at the point of freezing. However, if installed on a metal pipe (better heat conduction than plastic) and then wrapped with insulation, I believe it could protect an area well past the end of the actual heat tape. Whether it not it can protect 10 feet away would depend on how cold it is and how well insulated the pipe is. If the suspected freeze area is uninsulated and exposed to the cold air and is subject to any wind or air movement, then I'd say all bets are off. It would not help you.
Always on the outside.
Yes, this product can be used on rigid plastic pipes.
The proper way to do this is to excavate around the pipe about a foot or so in diameter, then insert a section of large diameter pipe around that pipe, lie a well casing (pvc would be fine). It should stick up above the ground and have some kind of cover so rain/snow doesn't accumulate in the casing. Now you have your water pipe not actually buried in soil where critters can eat through your heat strip. Apply the heat strip, then insulate really well all the way to where it enters the house. I did exactly this, and it's worked well for years.