Are trades done on exchanges added to blocks?

Question

I found a few answers to this question here, here, and here, but my doubts weren't cleared.

Are trades done on exchanges added to blocks? Or are they only added once you withdraw the funds to your own wallet? If this is the case, how does the exchange decide on transaction fees?

Based on the above posts the answer to the first question seems to be "no". Most exchanges seem to work off-block. Now, is it possible that as a buyer one may be buying bitcoins that don't actually exist? How is this controlled?

If I misunderstood and all transactions made on exchanges are confirmed into a block, who sets the fees?

Any good articles or pieces out there to learn about the work behind the scenes of exchanges? I can't seem to find anything that addresses this.

Answer 1

Are trades done on exchanges added to blocks?

No.

Or are they only added once you withdraw the funds to your own wallet?

Yes.

If this is the case, how does the exchange decide on transaction fees?

Fees for trading are just a property of the exchange, transaction fees on Bitcoin transactions for withdrawals are just their choice to make. They might absorb that cost, or pass it on to the user depending on the exchange.

Now, is it possible that as a buyer one may be buying bitcoins that don't actually exist? How is this controlled?

It isn't controlled at all, you trust that the exchange actually has something to sell. There's no way of knowing if they actually do or not as a client or an outsider. They might be a complete sham, might hold only a portion of the funds they claim to, or they might be completely legitimate.