You might never know whether exchanges are already snooping on your activities and mind you, they are being mandated by law to divulge information if they help facilitate money laundering schemes and/or similar activities that fall within the same line. I'd rather get my coins mixed in a mixing service than rely on an exchange that would probably ask me tons of KYC documents before I get to withdraw my funds.
Ofcourse I am talking about using exchanges without KYC. Binance allow unverified accounts to make withdrawals upto 2BTC per day which is quite ok.
Which is being questioned by the US authority. Sooner or later, some countries they are still servicing would do the same, requiring them to get local license and conform to the laws and regulations of those countries until the 2 BTC withdrawal limit/day is removed.
About timestamps, who knows mixers too maintain logs of every mixing performed on their site. It is not difficult task in PHP to maintain such logs.
It could be, but the risk is less than having your coins tumbled in an exchange. I'm not saying that mixers
would not do that in any way, it's just they have the lesser chance of doing it knowing that the moment people finds out, they will immediately run out of business.