Using doppler radar to detect bullets
The HB100 is an X-band doppler motion detector that uses pulses at a few kHz repetition rate. You might be able to detect the speed of the projectile (about 10.7kHz from the IF output at very low amplitude) but it would be non-trivial to do so. If you're shooting from ~25m then the time available is enough to get a few hundred pings (only the nearest ones may be distinguishable from noise with such a small projectile, and of course there is a cosine error term with any doppler).

It's useless for measuring impact position. Personally I would tend to something more along the lines of gluing a piezo element or accelerometer to the back of a metal plate that is the exact size of the target area. Keep in mind that if someone actually fires a real firearm at the target, the accelerometer in particular may not survive.