We don’t yet know if survivors have immunity. There are many reports of re infection from inside China and Hong Kong, and that the second time around it’s worse. If true, that completely discredits the “herd immunity” strategy. We need a vaccine.
That is not true. All the articles I read said the re-infection idea is just a rumor. Any appearance of that was simply caused by faulty testing or releasing a patient before they were fully cured. This is a virus so your body will have immunity if you survive and clear the infection.
It is definitely true that like a lot of illnesses, symptoms may fade away and come back stronger later. But this is not a re-infection.