Can we use fee rate less than 1 sat/vbyte? Is it possible to create, sign and broadcast a transaction with fee rate less than 1 sat/vbyte?
Yes, we can create, sign and broadcast transactions with fee rates below 1 sat/vbyte. However, it requires some workarounds and such transactions will most probably not be mined because most full nodes do not allow such transactions in their mempools.
minRelayTxFee is an option in the bitcoin.conf file that can be used to change the fee rate required for mempool inclusion as explained by Murch.

These are the steps for broadcasting a low fee rate tx which I found in a reddit thread:

Pair HW wallet to Electrum

Use the paytomany command to create a transaction with fee rate below 1 sat/vbyte

Import the transaction to sign in Electrum

Run a full node with minrelaytxfee set to 1 sat (0.001 sat/vB)

Find low-fee peers

addnode to connect with the low-fee peers discovered

sendrawtransaction to broadcast transaction

Check tx in block explorer: https://sochain.com/


Related PRs:
https://github.com/bitcoin/bitcoin/pull/13922
https://github.com/bitcoin/bitcoin/pull/13990
Related question: What is the smallest fee you can pay for an on chain transaction?
Related options in bitcoin.conf:
incrementalrelayfee : Fee rate (in BTC/kB) used to define cost of relay, used for mempool limiting and BIP 125 replacement.
dustrelayfee : Fee rate (in BTC/kB) used to defined dust, the value of an output such that it will cost about 1/3 of its value in fees at this fee rate to spend it.