Yeah, a defender is absolutely allowed to move once he's established legal guarding position. Not seeing the change in the rule you are talking about.
The sliding under a player on the helpside defense is absolutely supposed to be a defensive foul now. It's not when the offensive player has left his feet, but when the player has started his motion. I saw at least one of those in the game last night and in the clip above.
In regard to the block/charge call in men’s basketball, the committee is proposing that a defensive player is not permitted to move into the path of an offensive player once he has started his upward motion with the ball to attempt a field goal or pass. If the defensive player is not in legal guarding position by this time, it is a blocking foul.
Men’s basketball rules committee tweaks block/charge, Women’s committee adds 10-second backcourt rule