If you want quality pics similar to the type you've posted then you are going to have to get the tripod out every time.
Nothing wrong with them and you dont need a fast lens to take them.
The middle pic; the camera has exposed for the sky and left the trees dark. Correct this by using a graduated filter, but I don't usually bother with them, and use the grad filter in Lightroom 5.
For museum and zoo work, I'd definitely use the flash if possible. Once you start getting into the realm of fast lenses with apertures of f1.4 or f1.8 then you are talking big, big money.
I would buy a Speedlite replica for now, as this is your cheapest option, and see how you get on with it.
The new cameras do handle noise better but to what level, I can't comment on that, as I use a Nikon D80.