Is it possible to be immune to the coronavirus or develop immunity to it?

It is. That's how people that have gotten it survived. It's no worse than the common cold for people with a normal immune system. Their bodies naturally fought it off by creating antibodies that cured it. The people who have died from it already had some form of immune system issue, their immune system was weak.

Yes.  The 99+% who survive it will be immune to that strain.

To develop an immunity to a virus, you either have to have the virus and recover or be vaccinated against the virus. Even if you are not vaccinated, you may have a strong enough immune system not to become ill, just like the millions of people who don't get the flu every year. Young people generally have stronger immune systems than the elderly, which is why the elderly are more at risk from the flu or the Covid-19 virus.

The virus is too new for us to be sure.  If it's like most other viruses your body develops immunity to it, but we don't know if that's the case with this strain of Coronavirus.