a) B- and T-cells *are* you're learned immune answer. Both cell-types react to specific proteins or other molecules. In a case of an infection the body tries to identify proteins specific to the attacker (either virus or bacteria) and reproduce B- and T-cells with receptors for that molecule. After an infection both types of cells have some variants that live longer, these are memmory cells. The memory cells can in case of a new infection with the same virus or bacteria be reproduced very quickly. B-cells produce antibodies, that connect to the molecule they identify and destroy it. T-cells kill cells that show the molecule that they identify, in case of a viral infection they kill the cells of your own body that are infected and reproduce more of the virus.
b) Scientist don't know a lot about many things. Still, they also know a lot already and this current knowledge has already applications. For how long an achieved immunity will hold: too many factors are unclear yet. That doesn't mean we can expect a long-lasting immunity.
c) Maybe. You just said scientists don't know everything. There are different projections on how many people got already infected. You chose one on the higher end. So, what scientists really say is: *up* to 20 million may have been already infected. But maybe less.
d) As I answered in a, our immune response reacts to certain molecules. If a mutation changes these molecules, so that the receptors don't work anymore, you still need a new immune respone. Your immune system may react to multiple molecules from the infection. In that case changing one molecule will lead to partial immunity, as other receptors still work. Also some receptors may check for molecules, that are needed for the functioning of the virus, so that any change in that renders the virus harmless. But it is all a maybe, maybe your immune system only picks one specific molecule, maybe that can mutate and the virus will still work.