Can the firmware be updated over the internet, and can the device theoretically send sound over internet if the firmware is changed? If yes, that would be a dealbreaker for me (because, you know, crackers and the NSA).

That would require breaking the firmware encryption and signing schemes of multiple physically isolated processors, and even then it would be limited by the power budget, meaning transmitting audio data would drain the batteries very quickly. So, it is not completely impossible (what is, these days?) but extremely implausible and at the same time rather easy to detect; I'd say your (smart)phone is a much better attack vector ;)