I ask because they say in the email that their system will automatically detect the changes. Does that mean you're not supposed to answer the email that you made the changes they requested?
i reply them. even if it's just a small thing, i get their confirmation before going on. be paranoid, get everything confirmed. after all, it's their job to check your website. and they will do it whether you ask them or not. so why not show them your good will to cooperate?
yes. on most occasions, they thank me for my cooperation, there is nothing of importance about my sites, at the moment, etc.
It may take a few days, but I always receive responses from Google. And yes, I also recommend you let them know. Having your responsiveness on their files can't hurt you.