To check the balance.

The private key never sees the internet, but you can confirm transactions sent to the address you are monitoring.

You don't send coins to wallets. I kinda hate how confusing that terminology is and it's the biggest misstep that BTC has going for it.

When you "send" BTC to a "wallet" you are simply signing a transaction that gets annotated and then confirmed on the blockchain that says that xxx address is correct signatory for yyy amount of BTC.

The watch only "wallet" is basically like a temperature display. You've got a temp sensor that the display reads. The display cannot change the temperature outside. I hope I'm explaining that well.