Yes, but as the saying goes, anything can fly if you strap a powerful enough engine to it... so we've demonstrated basic capability, and the rest is now optimizing its performance a couple orders of magnitude.
Not at all. "Anything can fly", but not everything can fly without killing you. The fundamental problem is three-axis control with stability. A source of power does exactly nothing to solve that.
No, that just means you need a bigger engine. (And, perhaps, an inertial dampener, to survive the gees.)
Think of it this way: the more thrust you get, the farther you'll go before control problems start to manifest. Keep pushing, and eventually the rest of the craft becomes a rounding error in the math :).
