Yes. I’ve been using SFOS on my 10 III on top of Android 12 (latest available version) and with Android 12 binaries (v2a) for many months (see e.g. this post of mine from April) without a slightest issue. Before that I also tested it with Android 13, without any problems, either. Actually, I couldn’t notice any difference between 12 and 13. It is 12 that fixes some issues, and 13 just keeps them fixed.
Indeed, it’d be nice of them.
Well, that’s how it is. They only tested 11 thoroughly, 12 only slightly and 13 not at all, so they keep recommending 11, and that’s it. They clearly have better things to do.
They are. Many other people confirmed this. See e.g. this post confirming that echo and screen tint are gone.
That’s your very own choice. I don’t intend to convince you in any way and I really don’t care 
Please read the aforementioned thread, it makes no sense to repeat it. Android 12 and 13 fix (i.e. remove) issues like echo, not add them. As for mobile data, it has always worked for me, so I can’t tell anything about any possible improvements.