This rule is easy to memorize. = This rule is such that [for someone to memorize this rule] is easy.= It is easy to memorize this rule. = People can memorize this rule easily.= This rule can be memorized easily. (The last one here brings in the passive you seemed to be concerned about.)
The lesson is easy to understand. The tree is easy
Yes. It has to do with the properties of the adjective easy.
Interesting. I vaguely remember something from Chomsky that I learned in a class many, many years ago - I think he gave "He is easy to please" and "He is eager to please" as two sentences with similar surface structure but different "deep structure." You could, in fact, say "
easy to please = easy for someone to please him eager to please = *eager for himself to please others eager to be pleased = eager for others to please him