There are an infinite number of possible waveforms; pretty much any waveform in the electron field is a valid one. What we see as a single electron is simply a "spike" waveform localised in a particular position. There's no reason you couldn't have a more smeared-out waveform that was "an electron somewhere in the universe", though entanglement comes into play at some point.

When we have particular constraints (e.g. known energy) that constrains the space of possible waveforms. E.g. when we talk about there being an electron in an orbital around an atomic nucleus, what we actually mean is there's a waveform. of a particular shape around the nucleus.

Are you asking why we only ever see waveforms corresponding to whole numbers of electrons? That's the "quantum" part of quantum mechanics; certain values are quantized (e.g. electric charged). I don't have a good intuition for why that's so though, except to observe that the time evolution of a system preserves this quantization, so there's no way to ever go from having one electron to having half an electron (for example).