You could have been a little more specific. But in the 1st season, there was a 2-part episode when R2-D2 went missing and to make things worse, his memory contained ALL of the Jedi's military secrets. So Anakin and Ahsoka went to look for him to not only save the necks of the Jedi, but to save their friend as well.
Ahsoka
Yes
No, Ahsoka doesn't have any sentimental relationships in Star Wars: The Clone Wars
No. But, they have a strong realationship!
No
Dave Filoni; the director on Star Wars the Clone Wars
The name of his apprentice is Ahsoka Tano
Ahsoka Tano served as Skywalker's Padawan during the Clone Wars.
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)
Ahsoka's fate hasn't been confirmed yet, so we don't know.
Ahsoka Tano returns in season six, but only for a moment as a vision from Yoda.
If you mean Ahsoka Tano, then she is the Padawan apprentice to Anakin Skywalker in Star Wars: The Clone Wars animated movie and following animated series.