I don't think you can post 'anonymously' in the sense that there is no account related to your post, you'll always have to create an account, but you can of course use a one-off username and even email address if you want to. However, you can delete your account and then apparently all 'your' posts appear as "[anonymous]" whether you intended this or not. (And in this case, it seems the original poster just created this post with their usual, non-anonymous account, but then deleted their account.)
Charitable organisations generally do due diligence on large donors and will most likely do this in-house in most cases (perhaps with some external support) - very large organisations (eg Universities) will usually have a specialised in-house team independent from the rest of the operations to do this. It is also likely that at least the larger EA organisations did do due diligence on donations from Sam/FTX, they just decided on balance that it's fine to take the donation.
The answer to 1) is very likely yes as this was the case at previous EAG events in the UK. Whatever rules there are for newbuilds obviously a) don't apply to existing buildings (and the venue is not a new built) b) don't have any influence on how you use or label bathrooms at private events (unless you are discriminating or something which I assume CEA isn't planning to do).
While I would say $100mn is probably too high a bar, buying Whytham Abbey wasn't really $20mn expenditure as they'll sell it and get most of this back. So the actual expenditure (cost related to the transaction, running costs, overhead, gain/loss, not including any reputational cost) of the purchase is probably between $1mn and $4mn (depending on what they manage to sell it for).
In the UK, doing this would probably be counted as 'trading' and be subject to corporation tax, there is a common workaround, though, by creating a trading subsidiary that donates to the charity (allowing them to reduce their corporate tax burden). This setup might or might not be suitable for this specific occasion, and there are of course additional efforts involved in creating such a setup that might or might not be worth it.
Is this just a guess or do you have information on the actual costs of the event? (Just from their website, they seem to have various sponsors who are likely covering a substantial amount of the costs, and yes, their venue costs might be very low (or even close to zero) because Harvard/MIT are likely not charging them commercial rates, but that doesn't give any info of the actual costs and why they would be lower than EAG costs.)
Sure, I'm not objecting to policing language in general (there are certainly types of language that are inappropriate) or you making a specific suggestion of (gentle) language policying. (I just disagree with your specific suggestion on this - and I assume others do as well - and my point is that connecting it with you other suggestion - that I think more people will agree with - is suboptimal.)
I'm not sure whether it's good or not, but the main reason that it should be allowed is that it is impossible to detect. How will you know what someone's real preferences are?