Re: Testing! testing!
The whole tracing idea is really a red herring and about wanting to be seeing doing something. We are dealing with a virus that is extremely infectious (though apparently not contagious) with quite a long incubation period where people are infectious without displaying symptoms. This makes testing for the presence of the virus useful for studies only, because by the time you have the results, the damage has been done.
More importantly, we have to assume that the disease is endemic. This means that, until we have reliable treatment and a vaccine that it will continue to spread and the only thing you can do is control the rate of infection. But, unfortunately, it also means that those particularly susceptible to the disease will, at some point, succumb and probably die.
Reliable testing for antibodies should help us determine whether sufficient "herd immunity" has been built up in specific areas. The results from Sweden, which continues to have the most relaxed approach to the pandemic, will be key on this. At the moment the presence of antibodies does not guarantee immunity, because we don't know enough about possible reinfection rates, nor whether it will sufficiently suppress the virus so that people who are immune can be considered as no longer infectious. The hope* is that Sweden has naturally passed peak infection.
This is why both Norway and Denmark have decided to reopen schools and nurseries. Though, it's worth pointing out that people in Scandinavia generally keep their distance from each other anyway and a great many have summer houses they can escape to.
* Current death rate in Sweden continues to decline.