Regarding the slide from the loose ball, the player absolutely can slide from his initial momentum without penalty. And if he's on his back, he can even sit straight up legally. Just don't roll sideways.
As far as the player-control foul, and then double techs, consider it a false double foul, and administer them in the order they occured. Thus, you'd go with the possession arrow from the "T's" and put the ball in at half court.
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