Indeed they have. I've been studying them them for several weeks. The Germans used them for their V1 "buzz bombs" in WWII.
Very true, but I think the increase in power from the engine will more than make up for the loss in weight and power if it's designed well enough. For static and test/"proof of concept" runs, it won't be an issue. So, at least for now, this can be ignored.
We've already covered this, though very indirectly. He plans on using iris shutter valves which can function at extremely fast rates. It follows that if iris valves can and do function at those speeds, there must be an actuator that can also function that fast. The problem won't be speed, it'll be endurance. How many times can an iris valve be switched in rapid succession at high temperatures before it gives out? My guess is a lot more than a petal valve which has to physically bend each time it opens or closes and frequently gives out in a matter of minutes in a hot pulse jet. I think the actuator won't be a problem as a simple motor can probably do the job just fine. Since the combustion process in a pulse jet engine occurs at a constant rate, a stepper motor running at that same rate should be able to open and close both valves at the right time. It can be electronically synchronized with the pressure swings inside the engine.