Is it possible to make a heliostat with no moving parts?
The short answer is no.

You might be able to produce a curve that will reflect an arc (spanning the days extent from east to west) all day on a given day without moving it, but only a small portion of such a mirror will be going into your window at a given time, wasting the rest of its arc.  Further, (as the season changes) your north-south alignment has to change, although this change is much slower. 

A concave (focusing) mirror will have to be aimed to achieve concentration. Its focal length is a function of its curvature.   You can simplify your control to 1 axis by using a polar mount.

Have a look at some of the Heliostat sites