How good are entrepreneurial opportunities for faculty members? How easy is it for faculty members working at a reputable university to become entrepreneurs? 
If the faculty member sees an opportunity for a great product and wants to set up a small office with a few engineers working with one or two students, will the university sponsor such a venture? 
How enthusiastic or forthcoming will the industry and VCs in general be towards this? 
Lastly, how common are such professor-run companies for, say engineering faculty in top US schools?
This is quite common in American universities, and there are probably thousands of start-ups that have arisen out of university-based research. The question of financing such a venture is of course a challenging one to answer, but with the right contacts, is usually available. 

I can think of at least four or five such start-ups in the department I attended for graduate school, and I imagine there are several more in the planning stages.

As for how enthusiastic industry and VC's are, well, I think it depends entirely on the strength of the idea, and how "market-ready" the concept is. The sooner it's ready to go, the more enthusiastically people will flock to it.