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As long as you have NEO in your wallet, the gas is automatically generated. So yes, the gas does come 'free'.

What's the fee for transferring NEO from one of your addresses to another one of your addresses. For instance if i send 1 neo to myself without having any GAS will the transaction go through?

I think that should be free (I've not done but I believe I'm right).

the fee to move NEO From bittrex to the NEON Wallet was .1 Neo which I didn't understand; since bittrex won't send a 'fraction' of NEO Which I wish I would've known before I bought what I bought initially

I paided a fee of .025 NEO when transferring from My Bittrex account to my Windows wallet. Make sure that the net NEO after the fee is a whole number though!! i.e. 30.025NEO

I payed it too. Bittrex's fee is 0.025. So, If you want to transfer it, make sure you add 0.025 to your NEO balance to not lose coins.

If I send 2 NEO from a Binance account and pay in fees in BNB, will it send the full 2 NEO?