Hi,
I have my ZIL and ETH in Binance exchange.
Read somewhere that I should never keep my crypto solely on exchange.[/quote]
Exchange should be for immediate trading not a place to store your wallet for long term it's bad decision
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.
As long as you control or have the key it will be ok, it's always been not your key not your coin as a Crypto investor, your balance will become zero if you withdraw all your coins of course, but it should be your decision if you don't want to leave anything in an exchange.