[ClarenceBauer]

I am thinking about using a rock-dash/pebble-dash stucco exterior on a shed I'm building. Have never done it before but I like the look. What quantity/weight of 3/8 river stone is required to do a 4x8 panel? I've included a couple of pictures to show the size of stone and look I'm trying for.

In videos I've watched online the pebbles are cast by hand against the wet stucco. But these pictures show a wall that looks more densely packed with stones than the walls in the videos. Did this wall have the pebbles cast by hand followed by some sort of pressing with a board or a clean trowel?

And what is the nature of that joint? I assume it's for expansion or stress relief. Is it just a gap with backer-rod and then caulk?

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The densely packed stone are a precast panel I have done many pebble & shell Stucco textures & there is NO way to get a dense pack by hand applying Stone.
You can check with the local rental store to see if they have a Shell Gun, it will handle the smaller stones.

 

[ClarenceBauer]

So you can buy those panels ready-made and "hang" them on a building frame? Some kind of cleat system?

Yes, pre-cast panels are available they may not be cost effective for a small job.
Also, there may not be a manufacture located in your area.
You could make your own precast panels.