Turn on 2 factor authentication for your Gmail account and disallow any device that you don't want to have access. Then even if someone knows your password it will ask you (on your phone) for permission before granting access. Change your password as well. And periodically check whether other devices have been given access (possible if someone has access to your phone).
If you really think there may be spyware involved you should reset your phone as well (as long as it isn't rooted or really old, pre 6.0, in which case that might not be enough). Be careful not to change password and then reset though: that can look like the phone has been stolen and get you locked out for a few days.
But you've really not explained why you think this, at least not in a way I can understand. So all of this may be overkill.
Can't comment on odd noises on BT headphones - could just be a connection issue for all we can tell.