No, forced movement is not required to take place. It is also allowable to cause the creature to move less than the indicated number of squares, so long as a destination is not specified.
Pg 212 of the Rules Compendium reads as follows:
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.
When a destination is specified, it is absolute; the creature or effect must either move the target to that destination or not move it at all.
To put it another way, you could think of it as causing forced movement, but simply using that movement to move the target 0 squares.
There is no difference between pulls, pushes and slides in regards to not enacting forced movement, though obviously you cannot push or slide someone into blocking terrain such as a wall.
There is no difference in regards to source or type of the effect - again, think of it as moving them 0 squares.
You can choose to move the target less than the amount specified, so long as the description does not specify destination the target must reach. If the target cannot reach that destination with the distance specified, the forced movement fails altogether.
Yes, you can choose which targets you wish to move and which you do not in an area effect.
