First, Winter Orb
does say that it is "turned off" if it is tapped. Rather than looking at the text on the card, you should look at the Oracle text, which can be found at
http://gatherer.wizards.com. Since Winter Orb will be turned off during your untap step, you would get to untap more than one land.
Second, if you destroy Dark Depths after your opponent uses Vampire Hexmage to remove the counters, your opponent will
not get a Marit Lage token. The reason is because when its triggered ability resolves, it looks to see if he actually sacrifices Dark Depths. Since he doesn't (you destroyed it with his Strip Mine), the triggered ability will resolve and see that he didn't sacrifice Dark Depths, so he won't get a token.