I made a purchased of a vase, using one of those blank checks
The cred card company sends you. But they charged me cash advance fee.
On the purchase. Does that sound right??

Yes. Read the fine print on those checks. Using them is considered a cash advance, not a purchase. Generally there is a fee involved.

Yes that is what those are, They are not really "checks" and not issued on a bank. They are a request for payment from the credit card company and yes in every case I have see it is considered a cash advance.

So yes in every case I have seen that is how it works