Yes, an electron does take up a finite, near-point-like amount of space, as does the nucleus, but only if you measure it. If you leave it alone, the electron is everywhere around the nucleus. An atom is filled with smeared out electrons, which don’t occupy a particular near-point-like amount of space, but exist as probability clouds, who.
The model of an atom we get in school looks something like this:A ball made of balls, with lots of smaller balls zooming around it, right? And maybe you heard somewhere that if ..