Is it normal to get a password prompt after clicking "Restart Now" for a Mac update in settings?

Yes, if you have initiated a software update in the Software Update panel or even with an individual app, then this is expected behavior since macOS wants to confirm you want these things to proceed. Anything that will affect the system areas of the drive (or anything located outside of your own home user folder) will have macOS prompt you for permission to proceed. I'm not sure how it works if you have macOS configured to automatically download & install updates.

If you have not initiated the action, then it may be some malware that has accidentally been download. Although some of your installed third party apps may prompt for permission to install an update (some apps do, while others update themselves automatically in the background with no prompts for permission).

Depending how you have macOS and the App Store configured, you may sometimes get prompted for your AppleID password to update apps installed from the App Store.

Yes and it seems to work much like in iOS for iDevices where the Password is required to commence the download and Again before the Installation process can start.

It is basically verified Ownership of the Device as being You and You are the Owner of the computer