focal length – What lens do I need on a P & S camera to shoot faces?

Almost certainly more than enough in terms of focal length, but a point-and-shoot may not be enough to capture enough light and make the background blurry.

A little over 100mm (35mm equivalent) is useful for taking pictures of people standing at a distance of 10 to 15 feet. If you just want the face in the picture, maybe about 150 mm? Although you do not find these exact objectives, there are 85 mm and 135 mm; they just require a little more cropping. A full frame option is a telezoom goal, such as 70-200.

A 35x zoom on a compact camera almost certainly starts at about 30mm (35mm equivalent) and reaches about 1000mm (35mm equivalent). So the zoom is much more than what you need. Excessive, I would say. In general, super-zoom lenses are not the best for producing good images. They are simply better by zooming in on such ridiculous magnification ratios that the image will be so agitated that even image stabilization will not fix it.

But the big question is this: can a compact camera take pretty good pictures? You need a lot of light for such a small sensor. With the weak flash, you can not have enough light. Thus, a tripod and asking the subjects to stay still is necessary for useful pictures, although the image stabilization may perhaps in some situations be sufficient not to require a tripod. Image stabilization, of course, does not stop the movement of the subject.

A larger sensor camera, such as an APS-C DSLR / mirrorless mirror, is a much better choice because it collects much more light and can make the background blurry. You can find DSLRs at a very cheap price today, but the goals require some investment. For portraits, get 50 mm and 85 mm for APS-C. 50mm is very cheap, 85mm costs a little more.

Of course, the ultimate portrait camera would be a full frame camera, but I would say it's overkill for most uses.