I'm trying to meld my old rules knowledge (circa 2010) with the newest ruleset, and I can't quite figure out when to check for whether or not a character can/could have been knocked back.

So let's start with a simple example (assume all characters are the same size):
Scenario 1:

Target B has Charge showing on the dial, and Attacker A hits rolling doubles, dealing 1 damage, and Target B no longer has charge.

Do they take knockback?

Scenario 2:

Target B is showing Combat Reflexes and gets hit, again with doubles, knocking them onto a click that does NOT have Combat Reflexes.

Do they take knockback?

Scenario 3:

Is there ANY way to deal knockback damage to that regenisis wolverine that heals every click?!

Oh I forgot a scenario:

If A character is hit onto a click that has charge or Combat reflexes, do they take knockback?

You check for knockback from an attack at the end of step 3 in the attack sequence which is before damage is dealt. For other kinds of knockback, you Check right before the knockback happens.

Scenario 1 and 2 would not have knockback. Scenario 3 would require a figure or gameplay element that prevents other figures from preventing knockback normally. I could have swore there was something made recently that could do so but I can’t remember. Otherwise you would need to outwit Wolverine when he’s not on STOP and use someone who has a “can’t use” type of debuff for Wolverine’s STOP clicks.

If a figure is hit on to a click that would have charge or combat reflexes they would get knocked back because the check happens before they get damaged on to that click.

The Rebirth Black Canary is an example. She has this ability: So if she uses that, your team can knock Wolverine around even on his STOP clicks.

Knockback is checked before damage is applied.

So if they have charge or CR when you hit them then there will be no knockback. If they have charge or CR after they take the damage (but not before) then they will be knocked back.

Wolverine, as stated, has a power preventing knockback on every click, so you will need something special, like the Black Canary that was referenced, to knock him around.

Also, presumably if I outwit charge and hit him with knockback (on his first click) he would take knockback? (off elevated, because he has toughness) BUT you can knock him past a stop click that way?

Yes. Also, side note, STOP clicks don't stop turning the dial for knockback damage. That probably won't come up with this Wolverine, but just thought I'd mention it.

So if Wolverine were on the rim on click 1 and got hit for 1 damage by PW with a doubles roll, he would get damaged to click two, take two knockback damage and end on click 4 (because during PW he would have no charge and no toughness). His STOP on click 3 only stops the dial turning when taking damage from an opponent's attack, and knockback doesn't count.

If you outwit charge or CR them yes, they will take knockback.

If the damage clicked them to a stop click then the knockback damage will move them past that. It is separate.

Knockback damage is not damage from an attack. That is worth keeping in mind, too.

So does that mean knockback damage is not considered part of the attack? if a character were to die from knockback damage would it not trigger effects that say "when this character kos another character"? Or is it still considered KO by the character just not KO as part of the attack, like poison?

No, a character KO'd by knockback doesn't count as KO'd by the attacker. For example:

I know this, but what if they are knocked into a wall and onto a CR click? In the olden days CR would prevent knockback damage as well I believe, but in 2019 do I take the extra point of damage?

It's is not the olden days anymore.

CR says nothing about preventing KB damage in its current form so it doesn't prevent KB damage.

But, if you really want to know...