You use a move that increases your stats (example: Swords Dance). Then when you use Baton Pass the Pokemon that you swap out for will gain the stat boost even though Ninjask used it. Speed Boost does not work with Baton Pass.
Yes it does;
every effect on the Baton Pass user that isn't a status condition, both positive and negative, is passed on to the next guy. That means you can pass a Leech Seed, Substitute, Encore, as well as any increases or decreases to stats.
Yes it is. Maybe not in current competitive tiers, but I do see it pretty commonly, especially in Gen4 UU. Its great to set up a sweep. For example, a smeargle with spore/ingrain/bellydrum/batonpass.
I have a Baton Pass team. If you want to use Baton Pass team I recommend something called partial BP. Rather than building a complete team around BP, you have say a NInjask that can pass to a Rhyperior or Metagross with Swords Dance. The. The other three slots are Pokemon to use in case BP doesn't work out. Full BP is more complex with defensive stat boosting and Ingrain passing to block phazing.