Yes. The abilities simply allow you to move or shift "up to" a certain number of squares, and 0 is an allowable number. The fact that they are a Move Action is irrelevant.
This is the same wording used on Forced Movement (Compendium, Forced Movement):
When a distance is specified, it is a maximum; the creature or effect producing the forced movement can move its target up to that number of squares (or none at all). For instance, a character's power might say, "You slide the target 4 squares (or up to 4 squares)"; both mean the character can move the target up to 4 squares or not move it at all.
As for Acrobat's Trick, it will not provoke an Opportunity Attack because you never leave the square you are in. See the Compendium, Opportunity Attack:
Moving Provokes: If an enemy leaves a square adjacent to you, you can make an opportunity attack against that enemy.