Attempting to create a fake transaction without paying any fees and without it ever getting confirmed is not a practical scenario on the Bitcoin blockchain.
Correct. If the input is invalid, then the transaction is invalid and it will be rejected by EVERY node on the network.
While you might be able to create such a transaction and broadcast it,
Broadcast it to whom? Bitcoin nodes will simply reject it.
the likelihood of it being confirmed is close to zero.
It is exactly zero. Invalid transacitons can not be confirmed.
Instead, it will likely remain in the mempool (the pool of unconfirmed transactions) until it eventually gets removed by nodes after some time.
No. That is incorrect. Fake, invalid, transactions never get into the mempool in the first place. A transaction is verified BEFORE it is accepted into the mempool.
Further more, deliberately creating invalid or fake transactions . . . -snip- . . . may be against the terms of service of some wallets and exchanges.
How would a wallet or an exchange know that you created a fake transaction? Why would they care?