Probably shut the Rotax in my FD CTSW off 20-30 times in the pattern and executed a dead-stick landing. I have played with speeds to stop the prop and to let it turn over a blade at a time. With the 2.43:1 gear box the prop often turns a blade at a time at slower air speeds; ka chunk, ka chunk, ka chunk.
I've landed dead-stick with cross-winds a few times - not a big deal.
There is no mixture control on my Rotax so shutting down is always by the key. I turn it to one mag for a few seconds to let the engine slow down a bit - never have gotten quite used to the slamming stop in a Rotax.
One time I took the plane to 10,000 feet, shut the engine off and glided to 4,000 feet at book best glide to verify the glide ratio, which I determined was 8.9:1, much worse than I'd expected but a good number to know.
On the LD/Max flight and a couple of times in the pattern I've done a key air start. I have not tried to air start it by diving and turning the propeller.
The OP seems to to imply a more convention engine, such as a Continental or Lycoming. I have shut the Lycoming down in the air only as a part of ME training and checkride. On one occasion, the battery was too weak for the restart and we did not dive the twin to restart it; we limped home on one engine, which makes one's leg tired.
I did mag checks in the air in my T210. If the engine dies on one mag, one wants to be sure to pull the throttle before going to a good mag, otherwise one can build up the gas and get a backfire (just like you get when one inadvertently goes to "off" when checking mags on the ground).
I feel very comfortable shutting the Rotax down in flight, though I'm not sure how I'd feel about doing a very long glide where the engine got thoroughly cold-soaked. I restarted it on my LD/Max attempt at 4,000 feet so I'd have some time to fiddle with it if needed. Part of the deal there is it takes one hand to turn the key and one to manipulate the "choke" (actually an enricher) which means you'd want the plane trimmed pretty well to fly hand's off. And, in a really cold Rotax, sometimes you end up doing things with the throttle to start it. If the "choke" handle doesn't stay where you put it by friction then you suddenly need 3-4 hands, which might be more hands than I would like to be employing in a glide.