Why not? It is possible to configure a node to allow free transactions and zero satoshi outputs, then such node will accept transactions, that will never be mined.
Right. But that transaction will be rejected by other nodes and won't be propagated to the network. OP wants the transaction to be shown in block explorers (probably to scam someone). Since such a transaction will be rejected by other nodes, OP can't succeed.
It is not for scam but spam, I want to touch some fellows without a need to pay for it