Alright, this is my best attempt at recreating the logic, though it might not be perfect because it’s really hard to see some areas of the picture.
To answer your questions:
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That’s achieved through adding a noise to the UVs- it’s called a distortion shader. Ben Cloward has a great youtube video breaking it down if interested. The only difference is, it looks like he’s using a controlled version of the distortion method to drive a rotation instead of just the traditional add.
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It looks like he’s achieving this through the use of vertex colors. Individual leaves are pretty impossible to control- since you can’t rely on pixel or vertex data to reliably move an entire leaf. So, to get around this, usually you paint every leaf a different vertex color. These 0-1 values act as the perfect movement offset. Based on the movement of his leaves, it looks like he has painted the leaves very intentionally- like based off of their distance from the center- to drive leaf movement that appears in waves instead of completely random. You can also get a similar effect by just using a large world-aligned noise texture. You may see some slight distortion within the leaves, but this will achieve the same wave effect without all of the additional setup.