Need to explain that one!
Max.

Ripple voltage is approximately equal to It/C.
That works out to 10V.
That‘s a lot of ripple for a 12V supply, about 80%, not much better than if you hadn’t bothered with the capacitor at all.

But for a 100V 1A supply with 1000uF, it’s still 10V ripple, and now it‘s only 10% which is quite usable.

note: one normally assumes that t=1/2f, but it is less than that due to the time spent charging the capacitors, which increases as the ripple gets bigger, but it is a very useful approximation.

 

OF COURSE! As long as there is an adequate source voltage provided a linear regulator will remove all ripple at frequencies below it's frequency response limit. So that is an additional option available. BUT it does require a large enough capacitor to keep the voltage at least 3 volts above the regulator output setting.

And how warm is that regulator getting?

 

Even without the regulator, the ripple is negligible.

 

And how warm is that regulator getting?

It has a nice heatsink but the temp depends on the load, which is usually <100mA for building small test circuits. So the temp is also negligible.

 

Using an F-25X 12V CT secondary XFMR capable of 1.5A with a rectifier chip and 2200uF 50V smoothing capacitor

That will bump up the required TXMR Va for sure.
Max.