Reply #2: The person lighting the menorah.

[seemunkee]

And on the last night it is lit in the opposite direction.

Although re-reading what you said made me think that I had never seen it done from behind a counter like that. Usually I see the back of the person lighting the candles. I would still do it from the percpective of the person lighting it and then turn it around.
The person lighting the candles needs to say the prayer and have their head covered. Any hat would be sufficient.

Prayer
Ba-ruch ata, A-do-nai E-lo-hei-nu,
me-lech ha-o-lam, a-sher ki-de-sha-nu be-mits-vo tov,
ve-tsi-va-nu le-had-lik neir shel Chan-nu-kah.

I'm not Jewish but I married into it a long time ago.