Yes, the Ledger Live is completely safe and can be trusted by the users without any worry. While executing any transaction you will be provided with all the information of the blockchain network then you know exactly what transaction you are signing after the Ledger live login. So, you should not doubt the security of this wallet.
To withdraw money from your Ledger Live app, you need to sell some Bitcoin for cash on an exchange. Once you sell your crypto, you can move the funds to your bank account and then withdraw the cash as and when you need it. However, one thing that you need to beware of in this particular case is that you should have used the same bank account to buy your crypto assets.