I believe that I answered your question regarding the carrier icon..
It appears on the lock screen, but not on the main screen, that's a clock on the homescreen.
It's not an error, nor does it have anything to do with tethering, here on on any other phone, nor would there have ever been a connection between the two.
As to the unlimited tethering, it's your data so you can use up to your allowance for whatever need, tethering, not tethering, but that's got nothing to do with any phone, that's a network/carrier thing, absolutely nothing to do with any phone.
If you used half a Gb tethering on the Xperia 1, then put the sim card in the Note, you would still have used half a Gb tethering, why would it be anything else??
