Install on every instance. Import the same update set XML into each instance that should run the app — dev, test and prod — or retrieve it from dev through an update source. Every release contains the complete app, so you can upgrade from any earlier version straight to the latest.
Check your release first. Each version lists the ServiceNow releases it supports. Your instance's release is the Build name on stats.do, or the glide.buildname property. If it isn't listed for the version you want, contact Devolent before you import.
"External application" is expected. The app lives in Devolent's scope, x_devlnt_sch_atf, so Application Manager labels it an external application and won't let you publish it to your company's application repository. Move it between instances with update sets as described above.
Upgrading. Import the newer file the same way on each instance, starting with dev. Preview flags any records you have changed locally, so review those before you commit.
Extend it, don't edit it. Devolent owns the app and ships every fix and new version. Changes made inside the app's scope are overwritten or flagged on the next upgrade, and a modified app is outside Devolent's support. Where the app allows it, put your own logic in your own scope, where it survives upgrades. Need something the app doesn't offer? Contact Devolent.