You are correct that a snare slows the targets down for a set amount of time.
While looking at the tool tip of a skill that has a snare effect press the control key. This will give you detailed information on the skill including but the duration of the snare and the reduction of movement speed that will be applied to the target.
While it is possible that your skill with snare on it will have other effects, it is not usually a direct result of the snare component of the skill itself.
Lastly, no, not all snare effects are equal and pretty much all of them are altered in some manner through runes. You can use the tool tips with the control key mentioned above or even just browse snare causing skills from the link @heishe posted in the comment to the question (Like here is a snare skill with extended duration for a demon hunter: http://us.battle.net/d3/en/calculator/demon-hunter#b!!b)
Spirit Walk renders you invisible for the duration, although your "old" body stays where it was, and monsters can continue to attack it. If your "old" body suffers damage equal to 50% of your life, the spell ends early.
In addition to the invisibility, run speed increase, and the ability to walk through monsters, it breaks every and all effects that restrict movement.
It removes snares, stuns, jail effects, freeze effects, and any other effect, while making you immune for the duration (walls, however, still block you).
New monsters will "ignore you" if you pass by them, but are out of sight before the effects of the spell wear off. In other words, you do not aggro new monsters while spirit walking (although your follower or minions following behind could, if they don't wind up warping past the monsters to catch up with your increased speed).
One other undocumented effect is that you no longer take any damage while the spell is active, so you can safely walk through area effect spells (such as the effects of bosses such as Belial and Azmodan). Damage to your body after you leave it with this spell does not effect your overall health; it merely has the potential to end the effect early. If you are surrounded, are taking damage, and use Spirit Walk at 1% health, then the monsters continue to attack your body but do not hurt you. If the continued attacks would do damage equal to 50% of your health after you cast the spell, then the spell ends, but you are no worse for wear than the moment you activated the spell.
As an example, I used this spell repeatedly on Belial. If I was too close to one of the green pools indicating that he's going to take a swing at me, I'd pop Spirit Walk. His attack would hit my body, ending the Spirit Walk early, but I would take no damage from the attack.
Another major, major benefit to this spell is that you can pick up health globes while under its effects. This means that you can safely run through champion packs, rares, and uniques/bosses while low on health to snag some much-needed healing that would otherwise be far too dangerous to pick up (e.g. in the middle of multiple arcane lazers, molten magma trails, etc.).
Best Answer
The effect for the aura of Big Bad Voodoo works for your entire party. However, the Rain Dance rune specifically restores only mana. As such it will ONLY work for Witch Doctors but WILL work for allied Witch Doctors as well. Allies that aren't Witch Doctors will still gain all effects of the aura (including the mana regeneration), but since they don't use mana that part of the effect will do nothing for them.