Err, wouldn't it be (x+3)*(x+3), which would make the answer x^2+6x+9? The complications arise when h is introduced. But no matter. I've already turned it in.
No, it wouldn't. The Power Rule easily proves when f(x) = (x+3)^2, f'(x) = 2(x+3).
As for when h is used, as above, f(x + h) is usually used as part of the formula "lim(h-->0) ( ( f(x+h) - f(x) ) / h )", which, if f(x) = (x+3)^2, will equal 2(x+3).