1st I.E increases across a period, but the 1st I.E of Oxygen is less then of Nitrogen? why is this?

In nitrogen, the 2p-orbital is half full, which is the second most stable state after a full orbital, making it quite difficult to remove an electron. In oxygen, the 2p-orbital is neither full nor half-full, therefore the electron is more easily removed.

Neon is a small atom and has a complete outer orbital, making it very stable and causing the nucleus to attract the electrons with greater force, therefore its IE is very high. Copper is also quite small, but has only one outer electron. This makes the IE higher than larger atoms, but still lower than zinc. Barium is a very large atom, so the outer electrons are shielded from the attractive force of the nucleus, and thus easily removed. So your second grouping is correct.