Hideous Laughter can mostly be summarized as "fall prone & skip your turn"
As you noted, the target can take no actions while laughing.
Moving is an action (PFSRD):
The simplest move action is moving your speed.
So is standing up (PFSRD):
Standing up from a prone position requires a move action and...
Taking a 5-foot step ("shifting" in 4e parlance) is an action as well, albeit a weird one (PFSRD):
The following actions take a variable amount of time to accomplish or otherwise work differently than other actions.
Take 5-Foot Step
You can move 5 feet in any round when you don’t perform any other kind of movement. Taking this 5-foot step never provokes an attack of opportunity. You can’t take more than one 5-foot step in a round, and you can’t take a 5-foot step in the same round that you move any distance.
You can take a 5-foot step before, during, or after your other [emphasis added] actions in the round.
Attacks of opportunity are not actually actions of any sort (not even immediate actions) as far as I can tell, so the target can take attacks of opportunity by RAW (PFSRD), though this GM would deem that an oversight and disallow AoOs as well.
An attack of opportunity is a single melee attack, and most characters can only make one per round. You don’t have to make an attack of opportunity if you don’t want to. You make your attack of opportunity at your normal attack bonus, even if you’ve already attacked in the round.
An attack of opportunity “interrupts” the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn).
The part about not being helpless appears to be there to clarify that the target takes no defensive penalties beyond those imposed by being prone (PFSRD):
The character is lying on the ground. A prone attacker has a –4 penalty on melee attack rolls and cannot use a ranged weapon (except for a crossbow). A prone defender gains a +4 bonus to Armor Class against ranged attacks, but takes a –4 penalty to AC against melee attacks.