Hi Max,
though it is not possible to export the data directly, you can accomplish it by creating a custom template:
Copy the TR-AssignmentRecord.htm and replace the body with the following:
<body>
<p>!TERRITORY_START!</p>
<div>!TR_TERRITORY_NUMBER!;!TR_LOCALITY!</div>
<p>!TERRITORY_END!</p>
</body>
Please adjust the div part according to your needs (you find the available tags in the offline help). When the file is saved as TR-whatever.htm, then it is available in the print option Territories>Territory Record and you can use the Copy to Clipboard button to paste the data in a text editor and save it as CSV.
As to the second issue, currently it is only possible to use OSM (default) or Here maps in the territory manager (for printing Google is also available, but it is not used to display maps in TheocBase; see the section Geo Services in the offline help). It may also be possible to add support for the Esri or MapBox plugins, but please check the Here Geo Service first and also if Esri or MapBox would really help you further.
An alternative would be to use a third party GIS tool like QGIS and edit the maps and even territories there (you can link the theocbase database and could access the data from both TheocBase and QGIS). You could use georeferenced images, WMS or offline maps.
Another possibility would be to use a custom template for printing where you have a link to the territory's image (made up of some variables e.g. the territory number etc.).
Greets,
Marlon