1. Dogs (and sometimes rats) are trained to *do* search and rescue, so I'd counter propose something like [tag:lost-pet] instead. Its less confusing, and more.. laypersony

2. [tag:community-faq] is a bit of a special case of meta tag. Its meant for questions that are asked super often, and the goal is to build a canonical resource for similar questions. Quite a few sites have it, and its one of those things that should be more, not less.

3. No strong opinions here

4. It might be useful to consider in trying to merge - collars and harnesses are things that interface with pets. Leashes interface to humans. Folks often have strong preference with respect to all 3! I don't think leashes is the 'right' main synonym, but I can't think of a single simple english language option that covers all 3.