There is nothing like a fake bitcoin transaction been sent, this is only possible in if the bitcoin network gets compromised and you know how hard it is to do that. The other reason is if you broadcast a fake transaction it will be dropped or maybe except you have your own node or something like that and it is added through the back door.
This isn't accurate. You cannot compromise an entire network and even if you run your own node, you can't possibly convince another node to think that it is valid.
Is it possible create a fake transaction from a BTC address to another without paying any fee and also without this transaction gets ever confirmed?
I will explain the point.
for exemple I have a BTC wallet with 0.00001 BTC and I just want to send 0.00001 to another wallet in order to this wallet just see the incoming transfer but I want it to get rejected by blockchain, like a fake node input on blockchain, is it possible?
No and no. If you were to pay zero fees, you would probably violate the minimum relay fee requirement of Bitcoin nodes and that would mean that your transaction wouldn't be accepted and relayed by other nodes. If your transaction gets relayed by nodes around the network, then there is a chance that it would get confirmed. A transaction that can't be confirmed would probably not be relayed by other nodes.
There is no such thing as a "fake node input".
