Based on your translation of 'root face' I'm assuming that the bevel they are inspecting is a bevel that has been prepared for a groove weld between two pipes. If that's the case, the typical measurement tool, at least in America, would be a weld inspector's gauge like this one. There are various designs of gauge that do the job, but a Bridge Cam gauge is the most likely. It allows measurement of the bevel angle, the root face, and the alignment of the joint using different parts of the gauge. Under most codes, all of these are subject to inspection at the fit-up stage. It also allows measurement of assorted other things after the weld is complete, including undercut and convexity/overfill.
The part you use to measure the bevel can more generally be described as a protractor, but you wouldn't really want to tell an inspector or a welder to use a protractor. Generally a protractor refers to a larger device that is very difficult to use on thinner substrates or in tight spaces.
As for the question of pipe vs tube, I think you are correct in using 'pipe' for your application. In general american english, pipe refers to a round hollow section designed for fluid (water, air, oil, etc) to flow through. Tube refers to a hollow section that could be round, rectangular or another shape, but generally isn't designed for things to flow through it.
Do keep in mind that if the whole pipe is cut at an angle, that would be called a miter, not a bevel. A bevel specifically refers to an angled cut on the thickness of the material, in this case the thickness of the pipe wall.
More specifically in the structural fabrication world, pipe refers to a section that is manufactured in sizes corresponding to the Nominal Pipe Size standard. In this system, the pipe called 1" pipe actually has a significantly larger outside and inside diameter for historic reasons. Tube would refer to a steel section made to any other round size (usually a round number of fractional inches.)