Question

Have all kinds of atoms been discovered?

Answer 1

Atom in itself is only one kind. We cannot differentiate its type. All the atoms are made up of Proton, electrons and neutrons. The Number of proton is always equals to number of electrons. But yes We can say that atoms of different elements have different number of protons , electrons and neutrons.
It is difficult to tell the discovery of all the elements known to us right now. This is available in encyclopaedia.