Where to declare an API key?
Eventually things got fixed, learned that you can just add a .js file into your module with the HOOK_init() since they get stored to use at a later stage.

What obviously was causing the problem, was the wrong declaration of the API key, this was fixed by adding the line:

drupal_add_js("https://maps.googleapis.com/maps/api/js?key=[MY API KEY]", "external");


to the document.
After that, I could call the .JS file with:

drupal_add_js(drupal_get_path('module', 'maps_markers') .'/maps_markers.js');


More information on how everything was fixed can be found here:
Module conflicting with JQuery