Hi!
The answer is no to #1 and #3, but yes to #2. The AEM integration allows you to search, license and download assets from Stock in AEM, but it does not import your license history (question #1), nor does it automatically download assets licensed outside of AEM (question #3). However, if your search in AEM includes an asset that was licensed anywhere (in AEM or on the Stock site or elsewhere), it will show up with a blue checkmark (question #2).
As background, we originally planned to import license history as part of the integration, but we were told by the AEM team that disk space is at a premium, and since some customers have tens of thousands of licensed Stock files, automatically importing them could overload AEM.
Instead, only assets that you license inside AEM directly will be imported. Otherwise, you can search your licensed assets one at a time and import them manually. Or if you have a development team, I could assist them with creating an API script that downloads all the licensed assets to a local folder, and then you could use an AEM bulk import method to upload them--but this would require additional development work from your team.
Thanks,
Christopher