You are correct about Aballonian. It's a free action that is triggered whenever you make a check to maintain a grapple. You do not need to succeed on the grapple check. If it required you to be successful in the check it would have said so.
Pain Binding is different, however. It is activated as a standard action, and it allows you to make a single unarmed strike as part of that standard action. You cannot activate the ability if you make an unarmed strike by any means other than using the Pain Binding ability as a standard action.
For something like this you need to look at the whole text. There is no general rule for this type of thing and each ability can be different.
In the case of pain binding, it specifies the creature struck. If you fail the attack roll you do not strike the creature. So, for pain binding you have to succeed.
Spark states that you can use it on the creature you are grappling. In order to maintain the grappled condition after the first round you must succeed at the grappling roll. If you fail the check to maintain the hold the target no longer has the grappled condition. Since the target is no longer grappled you cannot use spark as a free action against it.
There may be case when you do not have to succeed on the check. There are a lot of combat abilities that say something like when you make a full attack. In the case of retributive kick, it actually states “and your first attack misses or is blocked, deflected, parried or otherwise cause not to hit the target”. So, obviously you do not need to succeed at the roll to hit.
Spark states that you can use it on the creature you are grappling. In order to maintain the grappled condition after the first round you must succeed at the grappling roll. If you fail the check to maintain the hold the target no longer has the grappled condition. Since the target is no longer grappled you cannot use spark as a free action against it.
Now that you mention it, this ability is unclear. I was presuming the spark triggered before the check to maintain the grapple resolved, which means you were already grappling it. But if it resolves after then yes the grapple would have to succeed otherwise you are no longer grappling.
Would you allow someone who is grappling to perform another free action before they make the grapple check when it is their turn? I have always assumed that when your turn comes you need to make the grapple check before doing anything else.
Would you allow someone who is grappling to perform another free action before they make the grapple check when it is their turn? I have always assumed that when your turn comes you need to make the grapple check before doing anything else.
Would you allow a player to use a free action to have their PC taunt the foe they're about to grapple, before doing the grapple?
Would you allow a player to use a swift action to have their PC activate some ability they've got that would increase their grapple bonus... such as an inquisitor's judgement?
Nothing in grapple says "at the start of your turn" or otherwise indicates it has to happen before any other actions. Legally, a PC could take their move action prior to the grapple attempt. Perhaps drawing a one-handed weapon or retrieving some magical bauble that gives you a bonus to your grapple attempt.