He can’t take uncommon lex’s chosen powers because lex only has them after a free action and amazo gets his powers start of turn.

The maximum of 1 damage is a passive, not a reducer. He can roll for Impervious, if failed check if damage is higher than 1 and it becomes 1

Amazo takes full damage from single target pulse wave? I don't see protected: pulse wave.

Yes. Even if you choose PW for Power Adaptation, you won't be able to use Android Body when targeted by PW, because of how PW works.

So with Power Adaption, he can't take special powers but can he take standard powers granted by special powers? Thank you.

Yes.
As long as the character can use the standard power (regardless of additional condition) Amazo can use that standard power (with any additional conditions) if the player chooses that power.