Sorry no one has replied for so long, but here goes:
yes MiFi units can create local WiFi, but their size means coverage is often limited. They are effectively mini routers in their right, but maybe slightly under powered if the plan is to stream lots of video from a local storage device.
You can buy a more dedicated mobile router, or even some ADSL2+ and Ethernet routers support the plugging in of 3G or 4G USB dongle.
The routers that take just a SIM are generally very expensive, but TP Link routers
that you plug in a USB dongle are pretty cheap.
For areas where people like EE are talking about using 4G for home broadband believe they are looking at devices like this
Can't help much more, as only 2G in this area, so the 3G/4G backup stuff tends not to work due to poor signals.