MS Outlook Web - how to download mail from outlook web

You can drag and drop emails to add them as attachments as a workaround (see this answer). You can download an email like this:

Start a new message

Click to edit the message in a new window.

Select all emails you would like to download.

Drag the emails to the new message. This will add them as attachments.

Click the down arrow on the attachment and download the email message, or send the message to yourself and then download all attachments.