Welcome to the Q&A Forum

Yes. A 302 is really only acceptable to use after a POST, where you're redirecting the user (no engine will ever submit a form). It's considered a "temporary" redirect and, in the distant past, Google would actually have problems with it. A 301 should be used for any other kind of redirect, especially when redirecting the non-www to www.

Ask the people who answer the telephone at the business office of this website.  They usually know the crazy ways that people ask for the product and the many alternative names used for them.

If you 301ed last week there may be some normal instability in your rankings... but should recover soon. Just to be sure that you didn't screw up go out and look at some of your old URLs to be sure that redirects are working properly.