"Do crypto debit cards report transactions to tax authorities even if the user lives in a third world country?" It depends. Many crypto debit cards partner with financial institutions, and they may be required to report transactions. Regulations differ in each country and some are part of international agreements that track crypto transactions.
"How do tax authorities in third world countries find out if someone maybe using a crypto debit card?" Some ways they can track are: if you used an exchange or through blockchain analysis.
"Is there complete privacy even in third world countries?" There could be if you use privacy coins like Monero and non-KYC exchanges. Complete privacy takes effort.
"What if its a debit card which simply doesnt have a user name?" Again, transaction data can be traced through blockchain analysis or links to an exchange.