In Attack of the Clones, when Anakin and Padme decide to rescue Obi-Wan, C-3PO is in the ship with them. Does the novelization or a deleted scene or something explain why he was there? Did Anakin steal him? Did the Lars give him to Anakin? Did Anakin claim legal ownership?
Per the AOTC Junior Novelisation
"Padmé looked at Anakin uncertainly, but he only nodded and rose to his feet. They made a hasty farewell to the Lars homestead, and Owen told Anakin to take C-3PO with him. Then they all hurried back to Padmé’s starship to play Obi-Wan’s message.".
A similar scene takes place in the official novelisation, albeit slightly before Anakin arrives;
“Well, Padmé,” Owen said, and when she turned to regard him, Padmé saw that he was grinning widely. “I’m returning this droid to Anakin. I know that’s what my mom would want.”
Padmé smiled and nodded.
So the answers to your specific questions are yes, no, yes and apparently (albeit the Jedi don't typically own things).