When I cannect another phone to my phone by bluetooth tethering, to use my phone's data internet, the data internet icon (4G) disappears and no longer is connected (while data is on).
What is wrong with my phone?
I just encountered this same problem. I fixed it by following this blogpost, basically at the bottom he describes that you need an extra APN setup just for the tethering. iOS has a dedicated tethering APN setting, but for android, you need to add one for yourself.
I had to add an extra APN where the APN-type was "dun". After I added this one, tethering worked for me and the 4G icon stopped disappearing.
id just recommend setting up a wifi hotspot. http://www.pcadvisor.co.uk/how-to/mobile-phone/how-tether-google-android-phone-image-3279408/