Welcome to the forum!
For node handles, it is not possible to set those precisely. Most people never have such a need, and this is the first time I've heard this question. May I ask what it is you're working on, which needs precision for node handles? There's a good chance there's a way to accomplish what you want, without depending on the node handles.
It IS possible to set angles and distance (length) for paths. Typically one would use Object menu > Transform, and then choose whether you want to Move, Scale, Rotate, Skew, or use a Matrix. There probably are some extensions which can do these things, as part of their particular features.
For node handles, I've sometimes used Snapping and a pixel grid (or guides intersections), to accomplish horizontal (or mirror) symmetry. Although in many cases, one needs to make some calculations. But I don't use it to set precise length of handles, or angle. Just to make one side of the something the same as the other. Info on snapping:
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Snapping.htmlYes, there are different ways to change the units. On the control bar for whichever tool you're using, for example, Selection tool
or Node tool
, and this will change the units for the object you're drawing. In Document Properties > Page tab, at the very top, Dispay Units, and that changes the units on the rulers. And it automatically changes the units in some other places, but not every place. Further down on that tab, you can change the units for the page size. And various dialogs allow you to change the units used by that dialog. For example, the Transform dialog that I mentioned, allows you to change the units for the features provided by that dialog. Grids can be custom configured in Document Properties > Grids tab and that includes changing the units for grids. If you double-click on a guide, the small dialog comes up and you can change the units for guide placement there.
I thought there was a way to change from degrees to radians, somewhere in Inkscape Preferences, but I can't seem to find it. It seems like some people might want to see radians in the status bar, when they change angles. But maybe I've just overlooked it - maybe someone else will know where to change it. The rotate tab of the Transform dialog shows a few options, including degrees and radians. I'm just not sure how to change what the status bar displays. Changing the display units changes the distance/length in the status bar. But I'm not sure about angles.
Well anyway, if you could explain what you're doing on the canvas, we can probably find a different process or technique to achieve what you need.