If you use bank transfers for these types of transactions, then the bank has access to all bank transactions, and in my case, that means that the tax office, as well as the financial police and maybe a few other agencies, have access to the same transactions.
Yes, but it still is better, in nearly every way. First of all, the authorities do not know that you bought or sold bitcoin. They can only found out about it if you report them what you did. If you're worried about that, you can still report everything normally, and just know that you'll buy and sell with no bullshit that has to do with "tainted coins". The only pro that a CEX can offer to you is larger volume, and buying and selling large quantities which cannot be done peer-to-peer easily.