You are correct on most counts. Office Pro Plus is just a different packaging of services from the enterprise tier.
I'm not sure what you are seeing, but if you can't purchase the pro plus SKU thru your tenant I would contact Microsoft. There are some subscriptions that can't be activated in the same tenant, but usually, it's just a configuration thing they can sort out on the back end.
Office Pro Plus has the Outlook version you need. However, it only includes the office client, and onedrive for business (which comes with SharePoint online subscription). If you need mail, skype, etc you should be looking at the E3 SKU which contains the same features as business premium, but also the pro plus Office SKU. In addition, there are some enhanced security controls thrown in there as well, so consider looking at enabling rights management service to be sure you get the most for your money.
As for OWA - that's just the way the interface works at present, there are no settings you can change to modify this behavior.
Edit
As of 6/28/2016 Microsoft is rolling out the ability to view Archives and manage retention tags (personal) in Outlook Business Premium.