wonderings

so like-signed electric charges repel one another, right? and an electron isn't actually a point charge, but rather a big bundle of charge spread over a region. why doesn't the electron repel... itself?

why doesn't all that charge just sort of spread out into space, like a sphere of pressurized water would disperse in lower pressure water? what's holding it together? and wouldn't the energy required to hold that bundle of charge together grow to infinity as we went towards the center and the "pressure" and "density" of the charge increased?

or does the electric field part of the electron really spread out like that, and the electron field just keeps pouring charge into the center? is that why an electron can influence things far away, at the speed of light, without photons--because its electric field is constantly growing outwards?