Hotmail to iCloud transfer problem.

It sounds like you have transitioned from a multi-account setup to a single-account setup with nested folders, which is causing the organization and signature issues you're seeing. When you create a single iCloud account and manually move Hotmail folders into it, Apple Mail treats those folders as standard storage directories rather than independent "Accounts" with their own specific settings.

To resolve the separation of your work and personal emails, you should ideally have two distinct iCloud aliases or accounts. In your current view, the "Work" folder is simply a sub-folder of your primary iCloud Inbox, which is why it doesn't have its own Sent or Bin sections. To get that "separate account" feel back, you would need to go to Settings > Mail > Accounts and ensure both addresses are recognized as distinct entities. If you are using one iCloud account for both, you can manage aliases at iCloud.com, but they will often still share a single Sent and Trash folder within the Apple Mail interface.

Regarding the forwarding issue, if you are only receiving emails from Apple, there may be a "Syncing Paused" status or a verification requirement within your Hotmail/Outlook settings. Sometimes, Microsoft requires you to "Verify" the forwarding address via a confirmation email before it begins sending third-party traffic. If the status in your Mail app shows "Updated Just Now" but the messages aren't there, double-check the Junk folder in both Outlook.com and Apple Mail, as forwarding can sometimes trigger spam filters.

For your signatures and notifying your contacts, you can automate the transition to save yourself the manual labor. In Apple Mail on your Mac, you can go to Settings > Signatures and assign a specific signature to each "Choose Account" on the left so it defaults correctly when you compose a message. To notify your contacts, the most effective method is to set up an "Auto-Reply" on your old Hotmail accounts. This way, anyone who emails your old address receives an instant message stating: "My email has changed to [your name]@icloud.com. Please update your address book."