The Durantium Refinery consumes durantium.  You'll eventually unlock mining upgrades for your starbase that will increase the yields.

No, you will consume/use/spend Durantium when you build ships or improvements/buildings, which use Durantium including Durantium Refinery. 

If you want to get more Durantium, you will either need to upgrade your starbase, which mines Durantium, or you will have to build another starbase, which can mine Durantium. 

Further in the upper right corner of the screen you should see a list of resources, which you harvest. Here you should see that you are harvesting/mining 1 Durantium. You can also see the Durantium used in ships and improvements/buildings. 

The mines mine it, the refinery refines it and the improvements and/or ships use it. You have to build more mining star bases to produce more.

Durantium is plentiful. You should have no problem getting more than you can use.

I guess it depends on how you look at it. I see the refined Durantium being spent (used) on the adjacency bonuses, maybe not ship augments.

Refining takes the base resource and turns it into something else.  Oil into gasoline, for example.

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