Hi,
I have my ZIL and ETH in Binance exchange.
Read somewhere that I should never keep my crypto solely on exchange.
Do I need (should) keep the cryptos in other wallet like MTW or MyCrypto? Will my balance on exchange become zero if I move? I am not sure about the procedure of that.
When you move your balance from an exchange to a personal wallet, your balance on the exchange will be empty. If your target is long term then it would be better to move it to your own wallet but you should really learn about how to secure your wallet. Make sure about your balance, calculate withdrawal fees, fees will make you receive less than the first balance, and this is normal things when you use exchange service.