QTC is a measurement for how much damping the box will give the speaker. .707 is considered "ideal" for sealed boxes. Higher qtc(smaller box) means an under damped box, or more upper end response and "punchiness" while sacrificing low-end response. As qtc gets lower(larger box), you gain more low-end but sacrifice the air spring support inside the box and at some point start sacrificing how accurate the sub will be. You must be using a sealed or bandpass box calculator because I have never seen qtc options in a ported box calc.
The gain value is a desired value that you put in as well. You won't find qtc or gain in the t/s parameters because they are preferences that you put in based on the response curve and performance that you're wanting. The gain value you put in is in db's, and is the value for how large you are wanting the peak of the response curve to be over the 0db reference line. A larger gain comes with a larger box and possibly higher tuning, depending on how the calc is set up. If it's a bandpass calc, the a higher gain means a narrower passband that the sub will be at that given gain value. IE: you can do a 0db gain and have a range from 25-80hz, or get a 3-4db gain, which will be louder, but have a narrower range of operation like 35-65hz. Personally I like to not have a peak in my response curve and just extend my low-end response as much as I can while keeping the response curve as flat as possible.
Sorry for ranting, I just kinda kept on going trying to not leave anything behind...I'm sure I messed up on something along the way.