Because the number of bitcoins is known is there any good analysis of if buys of BTC balances with sells of btc over time.
that is you should be able to sum within say 5% error over an extended period of time if the sells match buys.
Then you could call out fake sells and buys by exchanges.
I personally think and have said that a lot of exchanges are selling fake BTC and also a lot of fake tether buying.
Any decentralized exchange has to become fraction either by intention to suck profit in a harder currency from you, or because you just loose track
There is no such analysis and its impossible to do it. Number of buys always equal number of sells. Even if sell was made by non-existing BTC. The only way to spot fake transactions (not wash-trading but trading users-funds or non-existing funds by exchange) is to compare exchange hot and cold wallet with sum of all its users holdings. But you will have to have access to exchange books.
Here is a thread that may interest you - fractional reserve system implemented by crypto exchanges -
https://bitcointalk.org/index.php?topic=5094088.msg49096584#msg49096584
