Photography

Is photography real anymore

Just as real as anything else. It just happens to be a flat thing with tone and colour that you can look at, like a painting or a map.

Are we really capturing a true image of reality when we press that shutter release button, or is it just an approximation of reality?

A photograph is just an abstract representation of light and surface from a point view, it's up to the viewer to decide if it depicts something 'real'.

And, where / when do we (I, you, or whomever) draw the line between a 'photograph' and a 'graphic arts project'?

I useful way to describe photography is "lens-based arts" - that draws a relatively clear line in the sand.

Photomontage has also been a thing for a long time, one of the earliest examples being the Cottingley Fairies. Whether it is achieved in camera, in the darkroom or on a computer doesn't seem to matter much.

Lastly, while historically artistic value has always been a criteria for evaluation of a photograph, has this criteria changed now such that it allows for incorporation of elements which aren't real, or aren't possible?

This can be answered by responses to the other questions, but if you showed me a "pure" photograph, I could turn it around and show you a photograph that "isn't real" and describe the ways the light and materials have been manipulated along the way.

It's worth mentioning that truth and reality can exist in purely fictional compositions. There is no bright line between clearly real, or purely documentary, and total fantasy... it's a broad spectrum.