Sending email from multiple domains

As long as you have the domains verified in O365, you are OK to send messages. Selecting said addresses from within Outlook can be tricky though and depends on what kind of objects you have created. If you have added those addresses to a given mailbox, by default Exchange/Outlook will only allow you to send from the Primary SMTP address. There are some third-party tools/add-ins that can help with that, and that's generally the easiest way.

An alternative approach/workaround is to create separate objects for each address, either a shared mailbox or a DG would do. Then, grant yourself Send As permissions to each such object and select it in the From box when composing messages. It adds a bit of overhead, but it's the only "out of the box" solution within the suite.