Congratulations, you got it pretty right and on your own.

Tes, a typical PSU "makes" DC out of AC and the caps charge to peak AC voltage.
That drops somewhat afterwards under load, but, hey, Real World is where we actually live, so we´d better get used to that (and many more things

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As of transformer current raring yes, it´s good practice to have, say, 50% xtra capacity so as not to force anything close to limits.
As of the center tapped transformer, it´s a common way to get symmetrical power rails (voltages) and many amps work that way.
So if you ground the center tap and feed 2 caps in series, with their center "tap" also grounded, you´ll have roughly +/-16V supplies.
Just look at this 12W Marshall amp, which makes + and - 19V rails from a 14+14VAC transformer.
