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A1: Answers to both of your questions are covered in the rulebook by article 25.2.2:
A player falling, lying or sitting on the floor:
- It is legal when a player falls and slides on the floor while holding the ball or, while lying or sitting on the floor, gains control of the ball.
- It is a violation if the player then rolls or attempts to stand up while holding the ball.
Q2: Does a player bending down to pick up a loose ball but have one knee contact the floor and then rise up cause a travel violation?
A2: Yes, it is a travelling violation, based on the second bullet point noted above.