Zack is the leader of the group of X5s that escaped in '09. He made the descion to escape and split everyone up to make them harder to catch.
Once everyone was free he didn't give up his responisbility as leader. He dedicated his own life to making sure his siblings remained free of Manticore. Max infuriated him with her unwillingness to leave Seattle (and Logan).
Zack joined Max's raid on Manticore, against his better judgement, with Syl. He was captured by the X7s after the explosion. When he discovered that Max had been shot, he shot himself so they would replace her wounded heart, so she could live.
Zack wasn't killed though. Manticore replaced the organs they transplanted with biosynthetic ones, turning him into a half man half cyborg creature with his memories buried benieth months of brainwashing and reindoctrination. When Max rescued him, these buried memories were so confused that he tried to assasinate Logan, whom he blamed for putting Max in danger.
In keeping Zack from killing Logan, she accidently wiped out his memories. Knowing that what ever Manticore had done to her brother, would likely resurface if she remained around him, she set him up as Adam Thompson, a farm worker outside the city.
Title: Attack of the Clones
Title: Mind Games