Yes. Most MacBooks used in businesses don’t have an iCloud account associated with them. The store doesn’t work, but that doesn’t seem to be an issue.

Downloading and installing applications by dragging them from the installer to the Applications folder works fine.

Yes, there are few important apps that aren't available without Apple account, like Final Cut Pro or Xcode, but I don't use those.

Yes. But you'll be locked out of XCode-based development infrastructure (which arguably is a plus).