A lot of labs are working on that to evaluate the quality of the immune response. We can take for granted that there is some kind of immune response and some antibodies are being made following infection. We just don't know exactly the quality and the strength of these antibodies. Are they neutralizing antibodies, the kind of antibody that can really kill the virus when they meet the virus again, or are they just binding antibodies? We still don't have the answer for that.
As far as being reinfected, there have been a few case reports suggesting that some people might be reinfected. We don't know so far and we think it's most probably a person who had been infected. The virus was not totally eliminated from their body although they were not detectable in a couple of PCR tests, and then a few weeks later, they become detectable again. Most likely it's the same disease, but to date we haven't had a study that can definitely rule out that there hasn't been any reinfection. If it is, it is rare.