The way the world looks is very scary, and personally I wouldn't trust much of anything that any government wanted in my body right now, the social conditioning and excessive rules are enough.
Most likely no, ever get the flu vaccine? You get sick from it and there is no guarantee it will keep you from getting sick. Then you need another one the next year and so on.
I would have to guess yes, but not immediately. In terms of business owners (especially restaurants) people would most likely feel safe eating out again or going to stores in general as many people want to risk further spreading the disease. The economy would obviously benefit from this.
Vaccines will definitely help the same way it helps with the flu. At least, for the covid-19 strain. People keep making a point that covid will mutate. Yeah, the flu mutates every year, and every year we get a vaccine. Additionally, not all mutations result in something as deadly to humans as this strain is.