Can my opponent tap lands for mana when I have Sen Triplets on the battlefield?
Yes, activated mana abilities are regular activated abilities as far as Sen Triplets are concerned, and the chosen opponent(s) can't activate them. You can copy Sen Triplets' ability with Strionic Resonator, and you can choose another opponent with the copy, allowing you to tap lands from all chosen opponents with Piracy.

605.1. Some activated abilities and some triggered abilities are mana abilities, which are subject to special rules.


605.3. Activating an activated mana ability follows the rules for activating any other activated ability (see rule 602.2) [..]

As soon as Sen Triplets' ability has resolved, your opponent can't tap lands or activate any other mana ability, and if you cast Piracy later that turn, you can be sure that the opponent can't tap their lands in response. They could, of course, tap their lands and other mana-producing permanents in response to the Sen Triplets ability on the stack, especially if they know you are running Piracy.
Sen Triplets' ability is a triggered ability, so it can be copied by Strionic Resonator, and you can choose another opponent for the copy.

603.1. Triggered abilities have a trigger condition and an effect. They are written as “[When/Whenever/At] [trigger condition or event], [effect]. [Instructions (if any).]”