You need to differentiate between "action" and "main action" you mean "main action" here where the PHB in the section you quoted means any action at all. When we use the term "action" in this forum typically we mean one of the 12 "main actions"
If you read the PHB section on Actions, There are 12 "main actions". These mean actions include things like Magic, Attack, Influence, Study, Utilize, Ready etc. But these are not the only actions in the game. This is clear in the text of Actions:
"Player characters and monsters can also do things not covered by these [main] actions. Many class features and other abilities provide additional action options, and you can improvise other actions."
No not just from the list, which is a the list of main actions, but rather any action at all.
In the way this section is referring to action, it is talking about the thing you are doing in response to the trigger. The action you are choosing in response to the trigger when you "pull the lever" is "pull the lever", not one of the 12 main actions on the list. The action you are using when you "Ready a spell" is likewise "release the energy" as noted in the wording of Ready.
Yes, just like there is no "pull the lever" on the list of "main actions"
I think it is explicit and using the Magic action to cast it, when you have already used the Ready action is against the rules.