Question

How would you define ionization energy, electron affinity and electronegativity?

Answer 1

Ionisation energy = the energy required to remove 1 mole of electrons from 1 mole of gaseous atoms or ions

Electron affinity = the energy required to add 1 mole of electrons to 1 mole of gaseous atoms or ions

Electronegativity = the relative ability of an atom to attract an electron pair within a covalent bond

Explanation:

Ionisation energy

Ionisation energies should be defined with respect to the molecule that it being ionised. For example:

first ionisation energy = the energy required to remove one mole of electrons from one mole of gaseous atoms.

second ionisation energy = the energy required to remove one mole of electrons from one mole of gaseous 1+ ions.

While in practice, you might remove more than one electron at a time per atom or ion, if we're talking definitions this is the best way to set them out.
Electron affinity
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Electron affinity is just the opposite - it refers to the process of adding electrons to an atom instead of removing them. Hence, the definition also depends on what you are adding electrons to:

first electron affinity = the energy required to add one mole of electrons to one mole of gaseous atoms

second electron affinity = the energy required to add one mole of electrons to one mole of gaseous 1- ions
Electronegativity
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This is a different concept altogether. Electronegativity is the measure of an atom's relative ability to attract a bonding pair of electrons within a covalent bond.

Each element has an assigned electronegativity value (according to Pauling's electronegativity scale, which ranks fluorine as the highest with values decreasing down and to the left on the periodic table from fluorine).

So saying an element is highly electronegative means that when it forms a (covalent) bond with an atom with a lower electronegativity value, the electrons will be more attracted to the higher value atom, and will hence lie closer to that atom within the bond. (This can induce a dipole on the bond if the difference in electronegativity is great enough; and if the difference is greater than 1.8 the bond is said to be more ionic than covalent).