It is called a dead cut because you do indeed select the OFF position briefly. As Bose says this is not good for the engine if you do it at anything above idle and go back to L,R or BOTH causing a backfire etc
Not backfire. After fire. A backfire goes through the induction and carburetor. Afterfire goes out the exhaust. If you shut off the mags and turn them on again while the engine is turning, unburned mixture exits the cylinder into the exhaut, where it is subject to be ignited when the engine starts sparking again; the bang is in the exhaust. In engines at low speed with poor induction flow, a backfire is possible; in this case you're increasing the potential for not only damaging the induction, but causing a carburetor fire. A backfire occurs when the valve timing isn't perfect or when valve overlap occurs.
A better practice is a post flight runup, which should be done anyway, along with your idle mixture check. Lycoming and continental both recommend this, though few instructors know about it and fewer teach it. Again, a product of a heritage of inexperience.
These engines are prone to running on and the cooling plus cold air (actually mixture) will usually stop the engine. However in hot conditions the engine does sometimes run on lumpily for up to 5-10 seconds - the mixture being ignited by hot deposits in the combustion chamber.
An engine without an idle cutoff feature requires either fuel, air, or spark to be removed. When grounding the magnetos, spark is removed. By opening the throttle, the mixture is leaned to the point of cutoff, with the spark gone. It can lope and idle for an extended period on the idle mixture on the idle jet. By opening the throttle the mixture is leaned rapidly and any dieseling tendency to run on without ignition will be extinguished. If a magneto has failed to ground, then the engine will continue to lope, and may bang on you when you advance the throttle quickly.
I say this because im pretty sure the starter / solenoid would not survive being activated for the duration of a normal flight...
Actually the starter drive may remain engaged. Most systems are of the bendix design which should disengage when not under a load and at a high enough speed...but not necessarily the case. If the starter does remain engaged, what it becomes a generator at a high enough speed, and can experience damage or damage other components. The nature of the specific system determins this. Many aircraft use a single starter-generator which begins operation as a starter, but after cutoff and stable engine speed has been achieved, serves as a generator.
The starter solenoid is only used to deliver power to the starter; it's a remote switch. If the starter is engaged mechanically, the position or functiion of the solenoid is irrelevant. If you're talking about the starter bendix drive, which functions somewhat like a solenoid, but is not a switch (it's a centrepital clutch, in most cases), that's a different matter.
You ask about checks, but don't specify which ones. If you mean ensuring the swtiches are off prior to turning on the battery master, then yes, you should always do this. If you're asking if it's possible for systems to power up simply by turning on the battery master switch, then the answer is also yes. I've seen this happen on a number of airplanes due to various malfunctions. In that case, a stuck starter solenoid would not cause the engine starter to rotate, unless the starter switch was either shorted closed, or in the on position.
With the butterfly fully open, the fuel wont get sucked in to the cylinders (as much) because the venturi will be at atmospheric pressure, particularly during the last few gasps as the prop winds down.
Not exactly, but close. By opening the throttle plate, the draw from the low idle jet is removed. If spark isn't removed prior to this happening, the engine will accelerate and continue to operate off the primary jet.
However, on the rotary switch, selecting left and right may give you a drop but this only checks the L and R positions you have not checked the OFF position with this check.
If you have a three position switch and you've checked on the left and right positions, what you've already done is verified continuity and grounding of the P leads the magnetos ground out. You've already verified this, without checking anything else. By checking the off position, you're checking the switch, and nothing else.
Running it ICO runs it out of fuel and leaves some lubrication as one reason.
Mixture killing the engine doesn't provide any lubrication, and provides no lubrication increase over an engine killed by removing spark.
Turning the mags off leaves unburnt fuel in the cylinders which will strip the oil.
Oil continues to be redistributed as the piston moves up and down, and controlled by the oil control and scraper rings.