The purpose is not to lose sats on transactions.
You have to set the fee rate to 1 sat/vbyte and more and pay the transaction fee. Miners include transactions with zero fee only if that's their own transaction.
Unless you are a miner (or you own a mining pool), there's no way to make such a transaction.
Correct. Generally this type of thing is done for accounting purposes to move around funds from one internal address you own to another related address you own. Perfect example is the rather large sums moved around by exchanges & pools.
AFAIK, you have to use your own node to broadcast a 'real' tx to mainnet that has a usable fee attached to it and include your zero-fee tx with it to be sent to another address you own. For that matter, the 0-fee part can be payouts to multiple addresses - it's how most pools handle user payouts. The tx with fee does not have to be a big one, 0.0001 with appropriate fee attached would do it.
As for
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Are you planning to scam someone? And give him/her a TXID as your proof? Or abuse some websites that accept transactions with 0 confirmation?
I don't see any other purpose why you would like to make a transaction with 0 fees.
The comment is weak and mean.
No it isn't. It's a cold, factual and possibly valid assumption given that you have yet to give a reason for doing what you are asking about. It is highly unusual for a person to do. Many of us have been here for a decade or more and seen it all when it comes to scam plans...