Probably, but I wouldn't count on that for certain. It seems to just be a marketing label more than anything else.

Not necessarily. There are non-vegetarian animal products that could be included in a recipe that markets itself as "plant-based", e.g. gelatin, rennet, etc. It could even include a small amount of actual meat and say it's plant-based because it uses plants as the base of the dish. "Plant-based" is not a regulated term anywhere that I know of. I could sell a steak as "plant-based" by saying the cow was grass-fed. That advertising would probably not get me anywhere by way of customers, but it'd be legal.

If you mean ovo-lacto vegetarians then yeah, that's not how most of our neighbours down here understand vegetarian.