how can I tell if it is a Partner Development Org? Should it say that under company information?
It's been a while, so I don't recall if the word "Partner" specifically appears anywhere in the org, but an easy telltale is to look at Setup > Storage Usage. If you have more than 20MB of record storage, you're on a Partner Developer Org (PDO); you can see the different features in the documentation. If you have the now-standard 20MB of record storage, you're on a Developer Edition Org (DEO).
is it possible to use XML or any other way to deploy an app to the AppExchange without a Partner Development Org?
Yes, you can use a regular DEO to publish a First Generation Managed Package (1GMP), or you can use a Dev Hub's Second Generation Managed Package (2GMP). You do not need a PDO to host your metadata, although many partners do use them for that purpose. PDOs are meant for things like testing and demonstration purposes as well as development, which is why they have larger limits than a regular DEO. You can also now use Scratch Orgs, which are arguably better than PDOs, but PDOs are still supported, of course.