Proofreading the new Azure deployment article

Hi guys!

| Q             | A
| ------------- | ---
| Doc fix?      | no
| New docs?     | no
| Applies to    | 2.3
| Fixed tickets | -

This is a proofread of #3963 - just with minor (non-technical) changes for readability, etc. I made a quite a lot of changes, so please let me know where I made some mistakes - which I almost definitely have :). Ping also @hhamon!

Thanks!
App feels less formal to me than saying "application" everywhere. But do you think it's obvious enough for non-native speakers?