If the edges are tangent then if you have the "All tangentially connected edges" (expand the >> for that option in the chamfer dialog) selected and the shape applies then it will select the loop

There is a way to select faces, but not the way you are describing.  In the fillet command you can pick one face and then an adjacent one, but that is cumbersome.  You can also select a feature and it will radius all edges that way, but not a face as you describe.  This looks to be a good candidate for the Inventor IdeaStation

On the ribbon, click 3D Model tab  >  Show Panel icon . Select Plastic Part panel to display the Plastic Part panel, and then select Rule Fillet

I went through multiple websites with this data and ALL of them repeat the same bullshit. They have errors of one order of magnitude even within their own data. And literally, ALL these tables on the internet I found so far just repeat these same data with errors. Just have a look here:

I would like to select a face, either a flat surface, or a cylinder, and have a chamfer/radius placed at every edge of this surface.

Looking for a table with recommended chipload data, that is reliable and not bullshit. I am interested in data for small diameters 1-6 mm endmills and materials like: wood, acrylic, lexan, HPL high pressure laminate, engraving laminate, aluminium, anodised aluminium, MDF, HDF, melamine, plexiglass, etc. - common materials.

It seems like on most websites they miss one zero after comma for some data in inches, but not for all of it! And how can I figure out for which ones it is correct?

Check e.g. the chipload for 1/8" in aluminium (0,0025" lower limit) and compare with data for 3mm in aluminium (0,01 mm lower limit). Good luck cutting alu with 0,0025" = 0,0635mm chipload with 3mm endmill.

This iLogic creates a chamfer on already chamfered edges, which is shouldn't do, but I didn't bother trying to filter those out.