For the parts where you're evaluating at 2, yes, you can plug "2" in for "x", evaluate, and then do the mathematical operations.
For the part where you're "evaluating" at x, you'll need to work with the functions directly. But the operations on functions work the exact same way: Take the formulas, and do the operations with the polynomials or whatever, instead of which the numbers.
In this case, you'll be multiplying the two polynomials to get the answer.
Where did the "-3" come from? From what you did later, I will guess that the original function (posted above) is typoed, and that g(x) should be "2x - 3". If so, then your value here is correct.
Since f(2) = 7 and g(2) = 1 (assuming the correction above is correct), then f(2)*g(2) = (7)(1) = 7, so your answer is correct.
Since f(2)/g(2) = 7/1 = 7, then your solution value is correct.
Yes; the raised "o" indicates the composition of functions. (I will guess that you mean "F" and "f" to mean the same function, as well as "G" and "g".)
That's exactly right!