Lunge activates "before [the character] makes a close combat attack" (as per your quote), so first you resolve the movement from Charge, then Lunge and finally you make your close combat attack.

It works with Hypersonic Speed (same thing: movement from Hypersonic Speed, Lunge, close combat attack, movement from Hypersonic Speed - if there's any left).

Well, to be technical about it, Lunge still happens during Charge. It happens after the movement part of Charge, but before the attack part. In any case, Lunge is its own source of movement which is not linked to anything else in that it does not inherit properties of other powers or abilities from any powers or abilities with which the feat may be used in conjunction.

So the only way that a figure could Lunge from elevated to grounded, without stairs/a ladder, would be with the Cannonball feat as that feat gives the figure it is assigned to the ability to move from elevated to grounded during any movement.

And yes, Lunge can be used with HSS. Just remember that Lunge always happens before the attack is made. So if you start in base contact and want to move directly back away from your target after the attack, Lunge would not be any use there.

Remember to check the action sequence in each power that you're using. Lunge activates from being given an action that results in a close combat attack. With Charge, you declare a power action that allows you to move and then gives you a close combat action as a free action. With Charge, Lunge activates from the free/close combat action, not the power action. HSS is similar in that Lunge activates from the free action close combat attack, not the power action.

can Haymaker be used with Lunge? for example Hulk lunges 2 squares, not off a roof , and uses Haymaker to attempt to hit Lila Cheney

I'd Say if the Hulk did that I'd Call Shenanigans!

Ultimates Hulk(182) has Leap/Climb his entire dial and meets requirements for Lunge, and he has so he meets requirements for Haymaker. Is this sarcasm or have I missed something here?

I believe its because Lila Cheney is a pog and hulk should not hurt pogs.
additionally its a waste.

that's it, Lila is going to take a lot of damaage this weekend!