* I did indeed see a crow "anting" one time, and was initially as bewildered as the photographer in TFA. Surprisingly I was able to get much closer to the bird than they normally allow, but stepped back as soon as I saw it wasn't actually in distress.
* The best way to get close to a crow is to back up towards it; they are extremely wary of eye contact and will immediately become alert if you look at them or move towards them with your body facing forward. Over time, I used this method to get close to them and demonstrate that I wasn't a threat. I "trained" the crows to recognize that if they let me get close, I'll drop some food for them. After a while you don't have to do the backwards shimmy, but it's a good default strategy for approaching naturally skittish creatures.
* If you feed crows in exactly the same place every day, they will recognize you and fly to the "feeding spot". Crows pay very close attention to your movements and behaviors, and like most animals will try to develop a mental model to figure out when you're going to feed them. If presented with consistent causal behaviors, the birds will essentially train themselves.
* Crows are very sensitive to changes in appearance and behavior. I switched jackets one day and was met with immediate suspicion.
* My most fruitful experiment was right before the lockdown. I would stand in a specific location for a little while and watch the birds (watching them from a distance piques their curiosity and alertness to you). With them watching, I would pretend to plant food somewhere nearby and then move away. The crows would fly over, and I would immediately reward them. After a few weeks of this, I began gesturing towards nearby objects with my hand, and the birds would investigate the object immediately after I move away. After consistently rewarding this behavior, I was able to advance to "pointing to a semi-nearby object with my arm". One crow eventually figured out how to fly to the object I was pointing at, and I did a few successful tests to make sure the crow would fly specifically to the object I was pointing at, and not at some other nearby object. I have yet to train them to land on distant objects, but I'm hopeful!
* Crows like pistachios (they have multiple techniques for cracking the shell), and love cashews and peanuts (unsalted are best for the birds). They'll almost always opt for the "more convenient" snack, especially when they're competing with other crows. I try to reward the "bravest" crows first, by slowly moving away from the food pile until one crow moves in. Like other animals, crows also learn by observing the reward loop from a distance, and you can use this to get a large number of them to trust you.
* Crows are very curious when they feel safe, and it is mutually entertaining to set up unusual scenarios (such as hiding food inside or under tricky objects, like empty water bottles or closed paper containers).