Does Sarkhan the Dragonspeaker tap with his +1?
Yes, you'll tap him to attack, like any other creature. The same goes for any other planeswalker that's presently a creature (unless it has vigilance, as you've noticed), such as Gideon Jura &mdash; being creatures, they'll follow any of the usual rules for creatures.

This also means that when he returns to being a plain old planeswalker, he'll be tapped. Planeswalkers can be tapped! There's nothing saying planeswalkers can't be tapped. He'll untap at your next untap step, just like any other permanent.