Tube heaters:

Are tube amp heater circuits AC or DC? or either, depending on design?

Isn't DC better?

But, for AC heaters, does anyone put a switched diode in the circuit to fee the heaters some current when the amp is off, so speed turn on/ warm up time?
Heater's can use either AC or DC. Most amplifiers use AC because it is convenient to use for the small tubes as well as the power tubes. Preamp will have both. DC is quieter but if the AC is done correctly it works well. Some like it better.

Some amps and preamps will have a switch to turn the B+ voltage on and off. This is the main DC voltage for the tubes. The tubes heaters have a separate supply that can be left on whenever the component is turned on. It is easy to use a switch for this as well. If the heaters are left on, the tube will sound good quickly after turning on the B+.