You could actually send a completely fee free transaction, whether or not anyone will be willing to include that transaction in their block is a completely different question though.
Only if you mined it yourself. If you send a transaction with a fee which is below
minRelayTxFee, or the minimum relay transaction fee, it won't be broadcast between nodes. Nodes can set their own custom
minRelayTxFee, but most just use the default which is 1 sat/vbyte. If you try to send a transaction with a fee lower than this, chances are it won't be propagated through the network. It wouldn't be a case of miners not choosing to include the transaction, but rather they wouldn't even know it exists because nodes wouldn't relay it to them.
it is entirely possible to get by with 1-5 sats per byte if you're willing to wait hours/days for your transaction.
In the last few days I've been making 1 sat/vbyte transactions which are confirming within minutes. It certainly isn't taking days.