In addition to the target treating your allies as if they had concealment, does the Shaman's Nature Spririt ability Storm Burst (Su) have any affects on a target's ability to use ranged weapon attacks?
The Core Rulebook lists the varying effects that different levels of Wind and Percipitation can have. So it seems like the combination would impose a combined -8 penalty to ranged weapon attacks, and small creatures targeted would need to pass a DC 10 Strength Check to move if on the ground (DC 20 Fly - if airborne, with a -8 penalty), and Tiny creatures targeted would have to make a save vs. getting "Blown Away"
As the ability does not state it, no.
Don't infer that abilities do things that are not listed. It does exactly what it says, no more.
Does an ability need to say the effects that a condition has, when those conditions are defined elsewhere in the rules?
I ask - because, by your logic alone, the level 5 spell Control Winds and the level 7 spell Control Weather would also have no effects on things like ranged weapons and movement, as it does not say it does.
Incorrect. The Control Winds tells you to look at environment rules to determine effects. See here.
For Control Weather, they should tell you to look at environmental rules. Though, this is a case were they expect you to jump from the rules which tell you that you create a snowstorm to look up the rules for a blizzard in the the environment rules.
But storm burst does nothing of the sort, aside from telling you descriptively that it makes a small storm. It tells you nothing of how it should function, and is merely descriptive. The actual effect is completely described in the following sentence. In which it tells you that the target treats everyone as having concealment.
aha! thank you - missed those two little words.