photon-photon scattering is a thing but it's very weak.

No, Earth is way more massive than Mars and won't lose its atmosphere as easily. The upper layer of the atmosphere is ionized by solar radiation. Instead of simply stripping our atmosphere away, the solar wind would induce a magnetic field in this upper ionosphere. And this induced magnetic field would exactly cancel the magnetic field from the solar wind, ultimately deflecting the solar wind around Earth. This is exactly what happened on Venus and is one of the reasons why Venus still has an atmosphere.

The same thing also happens on Mars, but because Mars is significantly less massive it still lost most of its atmosphere over time from various processes.

But you are correct with your idea that Earth would lose its intrinsic magnetic field if the core cooled down and solidified.

My answer is a maybe.

There are a series of papers by Wu Siben from the 80s and 90s, like this one, that kind of assume it is a meteorite impact crater. The papers are pretty much all written by Mr. Wu and there seems to be little discussion of the question if it is an impact crater, it seems like he simply assumes it is one and then goes from there.

In contrast, there is this paper from 2017 by Xu et al. that clearly concludes that it is not an impact crater. Instead they found that the region is of volcanic origin. With the big ring structure perhaps being the remnant of an old volcanic caldera.

Personally, the 2017 paper seems much more solid than the old research by Wu. In particular the methods are much better.