A1 is running fast and dives for a loose ball on the
floor. She clearly gains control of the ball and then continues to slide
about six feet before coming to a stop and requesting a timeout. Is this a
violation? Why or why not?

No, it's not.

4.44.5 SITUATION B: A1 dives for a loose ball and slides after gaining control. A1 is in a position either on his/her back or stomach. What can A1 do without violating?

RULING: A1 may pass, shoot, start a dribble or call a time-out. Once A1 has the ball and is no longer sliding, he/she may not roll over. If flat on his/her back, A1 may sit up without violating. Any attempt to get to the feet is traveling unless A1 is dribbling. It is also traveling if A1 puts the ball on the floor, then rises and is first to touch the ball. (4-44-5b)