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
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Ahsoka sees a vision of her future self in the episode "Overlords" (The Clone Wars).
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.
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)
No, the first time we see Ahsoka is in the Clone Wars novels, then in the film. The novel came out a few days before the film did.
No, he's in love with Padme. He cares for Ahsoka, but just not like that.
Ahsoka doesn't love anyone