Ledger Hardware Wallet
As soon as you have set up your Ledge (which involves creating a backup seed, so you can restore your private keys in case you lose it). You can then create accounts (you can do so directly with Ledger-live or other third party apps which support the Ledger hardware wallet). The Ledger device basically is a keep safe for your private keys and allows only spending coins (any coins really this is not limited to bitcoin) if you confirm transactions on the device.
To your questions
If a transfer was success can be seen on any blockchain explorer (https://live.blockcypher.com/btc/) or directly inside apps like Ledger-live. You only have to know the address and you should be able to find it.
Coins will be transferred to your account anyway. No matter if you have the Ledger plugged in or not. You can not spend the money if you haven't attached the Ledger to your computer, because you can not confirm a transaction on the Ledger. (Ledger Nano X also has Bluetooth so you can wireless attach it)
If your hardware wallet stops working you can use your seed and buy a new wallet, like this you restore your private keys and you can happily spend your coins again.
The Ledger itself is protected with a PIN (min 4 - max 8 Numbers) which you need to open it up (like your mobile phone). So if somebody just randomly stumbles across it he can have a go at it 3 times then the device locks up and you need to recover your private keys by the initial seed). So what is most important to safeguard is your seed, if it gets stolen or public anybody who has a Ledger (or buys one) can get your private keys and spend your money.
Hardware wallets are a lot safer than keeping your private keys on any random device, as they do protect you very well against an online attack. Make sure you give your wallet address to people correctly. There is no bank to check your mistakes you make in misdirecting coins. If you send them to the wrong address they are gone. Your seed is an important factor and to be kept offline and save too (i keep mine on multiple usb-sticks encrypted inside a password manger, in my case key-pass which is password/key protected and stored offsite and protected against the elements, you can hammer it in steel, there is kits for that, or keep it on paper, to each his own)
First get yourself familiar with the coin concept and how it works otherwise it can be easy for scammers or malicious people to trick you into sending them money and you may loose it all. Ledger has a Ledger academy and they also feature YouTube videos, which are not a bad starting point to hardware wallets.
Full disclosure i own a Ledger Nano X and exclusively manage my crypto with it.