Clarification on whether electrons are "real"?

Well, electron is a "model". It used to be considered a particle, like a really small billiard ball. Everything seemed to fit this model, until some experiments proved that electron must also behave as a wave. Thus, our "model" changed.

The point is, we create models called "scientific theories" which accurately explain the behavior of nature, such as "electron theory". Once something is found that doesn't fit out theory, it must be revised, or sometimes even completely abandoned. This is what makes science awesome.

Electrons are as real as billiard balls, no less, no more. They both behave as particles and as waves, the only difference being that electron waves are very much longer than billiard ball waves would be. Quantum mechanics applies both to electrons and billiard balls, though we won't use it for the latter since Newtonian mechanics, which is much easier, is a very good approximation to how quantum mechanics says billiard balls should behave. If you could pack enough electrons into a ball the same size of a billiard ball you won't have any doubt about the reality of the electron ball. Of course there would be practical difficulties in making an electron ball, but these are only practicalities.