If I intend to have the character
behave and mapped in an certain way,
this would render the whole input
thing unnecessary, right?
Setting input binding may seem unnecessary if all you want to do is to press the spacebar to jump - a native event Space Bar → Jump is probably OK.
But it’s convenient to have bindings if you want to do a little bit more with it. Have a look at the custom MoveUp in your example - it’s bound to 6 (!) native events; pressing any of the bound keys / buttons will invoke the same MoveUp action with scale acting as its modifier. Otherwise you’d need to duplicate your script 6 times… or at least wire it 6 times to the same bunch of nodes.
[…] it should work with the InputAction nodes
as in my screen capture, then it
doesnt work for me. And therefore: why
and what should I do to make it work?
Both should work fine. What key are you using for screen capture and which blueprint is it processed in? Are you using capture key anywhere else? Input consumption is on by default, meaning that a keystroke is processed only once the blueprint that detects it first. But this behaviour can be overridden, too.
Assuming we’re talking about taking screenshots here, placing this in the Pawn or Controller is generally enough:

Providing you do not use the C key for anything else.
I need to make sure if 1) either the
blueprint with InputAxis nodes can
work by themselves or 2) if blueprints
can auto-generate input mappings under
Project Settings.
There is no such thing as auto-generation for inputs. You either define them yourself to make things more convenient, or use the native ones. If you ever see anything in the input bindings, someone added it manually - perhaps as a part of a template.