I have on the battlefield Will-o'-the-Wisp, and my opponent (it is his turn now) is going to attack in his combat step with his flying Air Elemental. I have to face this 4/4 creature and, in normal situations, I should not feel afraid of it. But I know – or I imagine that – my opponent has in his hand a Trickbind. The question is: may I sidestep this split second spell, by activating the regeneration ability of Will-o'-the-Wisp two times, in order to make sure it will survive the combat phase? In other words, I activate regeneration (B) one time, and then, retaining priority, I activate regeneration one more time (B again), sending to the stack two activations of the same ability.
Yes, you can do this.
After you activate an ability or cast a spell, you retain priority. If you activate the same ability again, the best your opponent can do is counter one of the two abilities on the stack (unless he has more than one Trickbind!) The other one will resolve and give you regeneration.
This works because although Trickbind prevents further activations of the same ability; with this method you are never trying to activate the ability after Trickbind resolves.
Yes, that would work. After activating the regeneration ability, you get priority:
117.3c If a player has priority when they cast a spell, activate an ability, or take a special action, that player receives priority afterward.
so you can activate it again. Trickbind does not counter any (other) abilities of the permanent already on the stack.
This answer does not cover the "sidestepping a split second spell" part of the question, but it does answer the "Possible way to counter" part of the question.
You can flip over a face down creature in response to a Split Second spell. So for example, if you had a Stratus Dancer face down on the field, you could flip it face up in response to counter the Split Second spell, protecting your Will-o'-the-Wisp, but that would be a bit excessive.
702.36e Any time you have priority, you may turn a face-down permanent you control with a morph ability face up. This is a special action; it doesn’t use the stack (see rule 116).
116.1 Special actions are actions a player may take when they have priority that don’t use the stack.
116.2b Turning a face-down creature face up is a special action. A player can take this action any time they have priority.
Split Second does not stop you from doing anything, it just prevents you from casting spells and activating abilities that are not mana abilities.
"The reason this behavior exists, is it prohibits your opponent from smoking your morphling with a lightning bolt when you declare you wish to unmorph. It makes morphing more useful." (Source: How can a Morph ability counter split second spells? Answer)