1) You would not be able to change the sentences without changing the meaning a little bit.
"She knew they'd fall for the trick" means she knew BEFORE she told them that the boys would dig more if she mentioned a pool. This sentence is giving you a glimpse into Lynette's thoughts prior to her statement as a first person point of view.
By changing it to, "They fell for that trick" you are changing the point of view to a third person narrator and making a general statement that the boys were conned into digging more.
1.5) You are right. They'd = they would
2) "Someone fall for the trick" would not be common. As it is with the verb "fall", it sounds like a command. And commanding someone to fall for a trick defeats the purpose of it being a trick. But the phrase "~~fell for the trick" is common.
Examples:
She fell for my trick.
Don't fall for his tricks!
I know they always lie, but I keep falling for their tricks.