For magic stone, I assume pebble is equal to small rock from table 4.21
Three of those would work in a pinch but I'd allow much smaller stones (actual pebbles), as well - unless there was a narrative reason not to, anyway.
except that the spell changes the 3 small rocks magically to each do different damage chosen by the caster?
Yes.
Would it be more clear if magic hurled ammunition was replaced with hurled weapon: small rock and the types of damage possible listed? It took me a while to find small rock to use with the spell
We don't automatically list spell components on gear tables. A lot of them are things you're just assumed to be near in appropriate environments.
and I saw one review mention this spell (the review saw that no damage was listed and noted it as missing text but I don't think that is the case).
The spell implicitly points to the damage types listed on pages 210-211. We're learning that folks want more (pardon the pun) spelled out and that's something we'll be doing more in future products. Of course, it will also mean less content in the same space, but such are the breaks.
Also, is the small rock magical because it does different types of damage? Or does it being magical have an additional effect?
We use lots of terms as keywords to trigger other effects, and to justify various things the GM may want to accomplish in the game. "Magical" isn't one that comes up a lot but for example I'd say, off-hand and not universally, that effects that target magical items might also be able to target these stones - though only until they're used, as after that they most likely revert - that's also left open to interpretation on purpose).
As you can see, the game intentionally requires GM and player input. We believe this is a strong feature that sets Fantasy Craft apart from a lot of other d20 games.

Finally, I assume each small rock get thrown one at a time. Does anyone run the spell differently (like getting to chuck all 3 at once)?
Take a look at the Ranged Combat Feats section (page 92).