The giant-impact hypothesis was widely popularised as a direct result of the Apollo samples, most notably by Hartmann & Davis in 1975.
It seems very likely that the Moon has a fairly uniform composition all the way down, because its physical density is compatible with that. And its lack of magnetic field also suggests there isn’t any metallic core at the Moon’s centre.
That is quite suggestive that the Moon is indeed a big chunk of Earth mantle which got knocked off at some point. It’s hard to think of another way to form the Moon with such a similar composition to the Earth’s mantle, but systematically missing all the siderophillic metals which the Earth has in its core.
The theory goes that the impacting body would have been entirely melted / vapourised in the collision, and got thoroughly mixed with the (now molten) Earth’s mantle before the mixture divided into the Earth and Moon. That bit of the theory is certainly the weakest link, and people still run computer simulations and argue about how possible it is. It’s hard to make it work – but not impossible, with a finely-tuned oblique collision.
But as things stand, the debate is basically over the details of the impact geometry. Nobody has yet presented any credible alternatives to the broad outline of the Hartmann & Davis model, despite it seeming to require extreme fine-tuning to give the right result.
I think Andy has already answered the question about the Earth’s orbit. Yes, the Earth’s orbit will have changed. But it found a new orbit. In the solar system’s early history, that would have been commonplace.