How do you know how many an atom contains and how many electrons the entire ion has either lost or gained?

If you mean how many electrons an atom contains then this is the same as the atomic number of the atom. For example, the atomic number of oxygen is 8 so it contains 8 protons. Since in a stable atom, the number of protons is equal to the number of electrons, oxygen contains 8 electrons.

If you have an ion and you want to know how many electrons it has lost or gained, you look at the charge. If it is a 2+ ion then it has lost two electrons, if it's a - ion then it has gained an electron. The number of electrons in an ion is the atomic number +/- the charge shown. For example a Mg2+ ion would have 10 electrons as a magnesium atom has 12 electrons and loses two to form the 2+ ion.

a) in form of conduction