This phone does all of the above you can send regular text messages as well as picture and or video messages. I have my yahoo and my gmail emails set up and they all work very well.
Yes, these features are on the ZTE phone.
Just went to this website http://www.zteusa.com/zte-unicolte.html
Saw this description in the overview(bottom 3 lines says what you are looking for):
The ZTE UNICO LTE is a 4G LTE Android 4.1 Jelly bean with 4.5” TFT screen technology with Haptic Touch and Google browser. Offering Bluetooth 4.0, Wi-Fi, and 1.2GHz Dual Core processor enough to make your internet high-speed. ZTE UNICO LTE comes with a 5.0MP camera, an expandable 8GB MicroSDHC™ card included. ZTE UNICO LTE allows users to use aGPS, browse the internet, take memorable pictures, send SMS, MMS, IM, and emails. Sold at Wal-Mart stores with no contract and unlimited data.
Yes. All that you list is standard features of any smartphone.