Moss-Pit Skeleton and Skyclave Shadowcat - sacrificing as cost of a triggered ability and triggering another ability when the first one resolves
Moss-Pit Skeleton can go back to your library after the ability resolves.
You are correct in saying that the ability on Skyclave Shadowcat includes sacrificing a creature as part of the cost.  The Skeleton would go to your graveyard and then the ability to put a +1/+1 counter on Shadowcat will go on the stacke.  At this point, both players would have to pass priority in order for the ability to resolve.  Note that the +1/+1 counter has not gone on Shadowcat yet but the Skeleton has already entered the graveyard.
Once the ability resolves, Skeleton is in your graveyard and therefore it's ability would trigger, allowing you to put it on top of your library.

Just to point out in your example, however.  Your statement

After blocking and before damage is dealt she wants to sacrifice Moss-Pit Skeleton to Skyclave Shadowcat (knowing that Kazandu Stomper stays blocked but no damage is dealt and Kazandu Stomper isn't damaged nor killed, that does not matter here)

If you replace Kazandu Stomper with a generic 6/5 creature, this statement would be correct.  However, Kazandu Stomper has Trample.  This changes how combat damage is dealt, and therefore Kazandu Stomper would still do 6 damage to you if it was attacking.