It's the end of the next half-cycle (the next zero crossing), but otherwise, yes; that's what happens.
Correct; they do not. Once a triac is conducting, it's very difficult to get it to turn off any way except removing the voltage across it (actually, it's removing the current through it that makes it turn off).
Right on. But think about how a half-sine looks -- a linear increase in on-time does NOT result in a linear increase in power delivered to the load.
There is exactly one "on" interval per half cycle; if it is very short, no appreciable power is delivered to the load. If it is nearly a full half-cycle in duration, nearly full power is delivered.
It's not noise; it's a regular string of pulses.
No; just an ordinary oscilloscope.
I didn't care about repeaters. What I wanted to do was control a large number of electrical valves for an irrigation system. As I said, the problem was that it was not repeatable -- the same number of "brighten" pulses did not always result in the same pulse width, and so I could not reliably select which irrigation circuit I wanted to run.
Honestly, I don't remember. I was doing this some years back. All I recall is that starting from "full dim" there was one narrow, "square" pulse, very close to the following zero-crossing. As "brighten" pulses were sent, that pulse always moved earlier in the half-cycle, but as it moved, it was joined by progressively more and more that looked just like it. The "extra" pulses occurred later in the phase than the one that turned the triac on, and so they had no effect on the operation of the unit.
Ripple would be a good term to use. The trade-off is that as you increase the time constant to reduce the ripple, you also increase the time the unit takes to respond to changes in the pulse width.
Yup.
Learn how to take old gear apart and scavenge the parts. Not only do you get all sorts of good stuff, but you improve your (un)soldering skills at the same time.
Isaac