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The moon does have a effect on Earth's oceans, but the biggest reason why oceans are active, is the variation of temperature both in the atmosphere and in the water(This also creates a variation on pressure). The difference on air pressures, will create wind, which in turn create waves.

Ocean currents exist because different places on Earth are at a different temperature, and therefore the water will feel a pressure force to go elsewhere.

This is quite a generalization, but meteorology is a complex science, and there is much to dig in.

Sure, but you didn't completely answer his question: the reason the oceans don't settle down is because the sun continuously drives these temperature gradients.

Some currents, like the Equatorial Counter Current (NECC) (which runs West to East just North of the equator) are actually wind-driven surface currents.

Yes it's about the wind (geostrophic currents) and temperature, but mainly because the earth doesn't stop rotating! The resultant forces are different depending on the latitude and depth. Note the dramatic differences on either side of the equator.

The most famous of these uneven forces is of course the Coriolis effect.