On this website https://ethgasstation.info/ you can see how many gas are recommended and also how much lowest gas is mined by the miner (currently around 0.1 gwei) But the chance for confirmation is very low.
Now for token, Actually I am still learning and don't really understand yet but i think that is also possible unfortunately I haven't found a way. You can see this transaction hash, he sent with 0 fees and i think depending on the token structure itself.
You can read here for the smart contract: https://www.coindesk.com/information/ethereum-smart-contracts-work/
And here for erc-20 https://www.investopedia.com/news/what-erc20-and-what-does-it-mean-ethereum/
Last thing, you can try reading the discussion about ERC865. So this will implement pay fee with tokens rather than eth, check here:
https://github.com/ethereum/EIPs/issues/865
Ethereum is very interesting to learn, Trust me and Good luck!!
It's could be hard these days to send transaction with 0.1 gwei, if it manages to go through, it might take days for the transactions to be confirmed, for me I don't think it is wrong to send your tokens and pay less than a dollars for the transfer fees, after-all exchanges charges higher for their withdrawal