I need to receive emails from trello, but not all the emails sent with the default settings. I don't want to know about all the activities that takes place on all our team boards, but just the activities on boards, lists or cards I'm subscribed to.
Is it possible to receive only these notifications, if I disabled the email notifications on my account page?
No, if you disable those email notifications, you'll stop all of them.
The notifications that you don't want to receive...are those cards or board that you can remove yourself as a member from? Alternatively, on a card that you've been added to, you can unsubscribe, despite being a member, and that will cut down on notifications.
The short answer is that you can't separate the notifications, and only receive subscription related notifications, but there are ways to cut down on notifications!
Default settings will not subscribe you to anything, but if you've subscribed to a board or card at some point, you would need to unsubscribe manually, yes. There's not a way to unsubscribe in bulk, unfortunately.
One feature you might be seeing is a current test we're running, where you'll be automatically subscribed to cards that you comment on. When you're writing a comment on a card, you'll see a checkbox below the comment box (if you're part of the test!) and can uncheck that to stop that automatic subscription.