I've got funds on Binance, if I send them now to the Ledger Wallet for Ethereum, will it go wrong? Or what can happen?
Your coins will arrive normally.
I really don't want to use the MyEtherWallet. I don't want my crypto to be online.
Your wallet won't be online.
MyEtherWallet is client-side. Your private-keys will NEVER leave the device.