... The moon does not keep the oceans moving. The impact did not "set the core spinning". I don't know who told you these things but they are not true.
Source: I am a geologist. But you can also just... google this stuff.
Firstly, the Earth's core:
The Earth's core is in two parts: a liquid metal outer core, and a solid metal inner core. The outer core has convection, caused by differences in temperature and therefor density - warm hot less-dense material rises, cools and becomes more dense, and sinks back down. This convection of liquid metal creates a magnetic field. It is this magnetic field that is driving the rotation of the solid inner core.
Nothing to do with the moon or a giant impact. Just electricity and magnetism. The core of the Earth already existed before the giant impact, and the giant impact did not touch Earth's core. The rest of the Earth was already rotating and thus already had rotational energy; it did not need an impact to give it this energy.
Next, let's tackle the Moon.
The moon affects tides, but tides are not ocean currents and are a completely separate process. Also, we'd still have tides without the Moon, because the Sun also gives us tides. They'd just be different and a lot smaller, about 1/3 the size they are right now.
But furthermore, tides and the Moon have NOTHING to do with ocean currents.
There's two main ocean currents: surface currents and deep ocean currents. They do not necessarily move in the same direction because they are caused by two different things:
- Surface currents are powered by wind.
- Deep ocean currents are powered by changes in water density, caused by differences in salt concentration and temperature.
None of that has anything to do with the moon and it never has.
The Giant Impact and Life
If anything, the giant impact reset the biological clock on Earth. We have no idea if this helped or hurt. Different scientists will give you different answers so we cannot definitively say "Life on Earth as it is now would not exist without the impact".
Generally, what life actually needs is huge swaths of time to develop undisturbed. A giant impact that completely devastated whatever pre-biotic mechanisms were assembling is not what I would personally call helpful, but some scientists argue the impact added a few last bits of essential ingredients to the mantle and crust that didn't get integrated into the core because the core was already formed at that time.
Now, moving on to Goldilocks zones aka habitable zones: you can get them around stars that aren't medium yellow stars like ours. Red giants have a habitable zone too. Most stars have habitable zones.
Science is currently expanding the definition of what a habitable zone is; if we look beneath the surface of the crust of a planet like Earth, we can find life! Microbes can live in wet rock too. Plus, there are potential habitable zones on moons orbiting planets like Jupiter, which is far beyond the ice line of a solar system like our own. But Jupiter causes strong tides in its moons which can create heat inside those moons, thus making them warm enough for water and maybe life.