My experience with this has been very good. The Bluetooth connection really will vary though, because it also depends on the quality of the signal of the transmitter (in the phone). Having said that, these headphones have worked very well for me and my son (iphone and Note 5). We can use them between multiple floors in our house, including down in the basement. I have a small house, but I would say at least 50 feet of consistent connection (may be farther, but thats about as far as I need).
As for the gym, it probably depends on what you are doing (jogging vs lifting, etc). They are kinda bulky (not overly heavy, just large), and would probably be cumbersome and get pretty sweaty too if it was anything high intensity.
Great headphones overall though. Hope this helps.