HI, I want to ask, Can a character with the KC tem ability move to a square adjacent to an oponent character with the KC tem ability without throwing the dice?
Also, Can you combine HSS and Exploit Weakness in one attack?; Can you combine HSS and Quake in one attack?; Can you combine HSS, Quake and EW in one attack?.

Well thats all. See ya

Yes. The reason you can is contained in the last line of the team ability -- "This character... ignore(s) this team ability"
No. HSS grants a close combat attack, and you need a close combat action to make EW work.
No, and for the same reason as above.
Still no, and still for the same reason.

A character with the KC team ability ignores the KC team ability so they do not have to roll to base another KC team member.

You cannot combine HSS and EW because HSS allows you to make a close or ranged combat ATTACK as a free action during your movement. EW is a close combat ACTION and therefore cannot be used with HSS. For the same reason HSS and Quake cannot be used together.

Finally, you cannot combine Quake and EW because they both require power actions and neither allow for the character using them to have an additional action as a free action.

Hope this helps.