ZOC = Zone of Control, you will see the city borders representing your colours, this is the Zone of Control, every Resource within this Zone of Control you are able to upgrade to produce goods for your empire.
Rushing is the term used for paying Gildar to instantly complete a building or anything else in your city's build queue. (See the first picture)
and I have no idea how I'm supposed to expand my boundaries to reach the mine without pioneers.
I recommend activating "Manual Improvement Placement" in the options, since it is pretty much "required" to reach it.