A:AnswerAnonymous,
As far as I could tell from my research, any Android phone (or tablet/device?) running Jellybean 4.3 or better should be compatible. I am using the watch with a Galaxy Note 2 on Verizon. (Carrier shouldn't matter as the watch is simply a Bluetooth accessory and doesn't utilize any additional airtime/data.)
A:AnswerYes with an asterisk.
Here's the official list from Samsung. Doesn't seem like the Verizon version is currently supported.
http://www.samsung.com/us/galaxy-gear-compatible-devices/
A:AnswerThe Galaxy Gear uses Bluetooth 4.0. Bluetooth 4.0 carries a max distance rating of 160ft.
The Gear will vibrate/ notify you if you have moved out of range of your smartphone!
A:AnswerIt depends, it's blue-tooth so if you're in your house it will probably cover you throughout, if you're at work it gets blocked by walls so the range is shorter, overall I'd say a good 50 ft.