AFAIK, a transaction must have all outputs above 5460 Satoshi to be considered as a non dust and have nodes relay it.
Wasn't it changed to 546 satoshis after the commit?
https://github.com/bitcoin/bitcoin/commit/6a4c196dd64da2fd33dc7ae77a8cdd3e4cf0eff1If it's below that, nodes would simply not relay it. There are nodes which relays it but for nodes using Bitcoin Core, they don't.
"for nodes using Bitcoin Core, they don't" except ones which uses custom script, right?
It is generally a bad idea to use 0 fees for anything below 0.1BTC since the priority would be so low that it would take a long time to confirm.
AFAIK isn't it 0.01
BTC which is considered higher priority with zero fee?