Unfortunately no. The address can be accessed without Internet connection, but your current account balance and any account management functions will be unavailable. Please make sure to have a stable Internet connection to manage your Fantom ecosystem assets.
Yes, smart contracts interaction can be signed with the Fantom FTM application. The current PWA Fantom Wallet does not allow you to interact with custom smart contracts, but we are working on it.
Yes, staking is also a smart contact interaction, but since it's a crucial part of the Fantom ecosystem, you can already manage staking from the PWA Fantom Wallet and sign it with Fantom FTM Ledger Nano S application. Use Stake menu item on the detail of you account to do so. Other parts are the same as usual transaction.
The Windows 10 May edition (Windows 1903) changes how Windows interacts with Ledger devices, leading to a security popup when using web apps. Please reinstall the apps on your Ledger device if you're experiencing issues when using web wallets.
Detailed information about the issue can be found on following Ledger Support page.