Anakin hugged Ahsoka because in that certain episode, she was killed by that evil unusual Force-being and she was resurrected due to the evil being's sister dying and wanting to give the last of her life to Ahsoka. At first, it seemed as if it didn't work, but she then came back and Anakin hugged her cause he was relieved to see that she was still alive.
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Yes Ahsoka Tano is an orphan because some bounty hunters killed them in front of her.
Anakin Skywalker just gave her that nickname in Star Wars The Clone Wars The Movie
It's very possible, but Anakin definitely doesn't because he is in love and married to Padme. Or.... I recall episode 2 season 2, which when Ahsoka was locked up, and Bane was trying to kill ahsoka or make anakin open the holocron, it went like this: Ahsoka: no master! Don't do it! Anakin: I can't let you die Ahsoka, that or we al laugh at their little fights and they seem to well compliment each other very well. That's my idea, Adri998 out :)
That episode is Season 3 Episode 16 "Altar of Mortis." (And actually, the only reason why Ahsoka turned evil was due to the living embodiment of the dark side of the Force corrupting her with a spell in an attempt to get Anakin to join the dark side)
Well, there was an episode in Season 3 known as "Overlords" where she saw a vision of her older self warning her about Anakin Skywalker, but that was actually The Son who was doing that, cause remember The Father said that he and his children could take on any form they wished. The Son was trying to get Anakin to himself