1) Login with Google is just a way to make it simpler for us for an MVP (and as you note we need the photos as we don't have a direct photo upload in this product just yet).
2) The graph is a reflection of intensity of the story (basically the more photos you take, the more interesting stuff is going on around you) and it gives you a time context for how things went.
We will definitely add an explanation in the interface.
3) What kind of customization do you mean? Structural (move things around) or cosmetic (colors, etc). Basically the graph is firstly a navigation tool. You click on the event names to move to that moment in all the views of the app (album photo grid/large photo view/album edit mode).
4) The map widget starts centered in Slovakia (center of Europe) for non-geotagged photos. This does not mean that the location was assigned to the album, it is just how the widget renders. (Does it look like we automatically assign the position? Any idea on how the map widget could look to avoid this confusion?)
For geotagged we are of course working on using this information (it is no there yet).
5) It is all about the context (graph - time context, info boxes - POI in the area or related concepts).
6) The problem with empty space in the timeline is that once you start 'stretching' and 'compressing' it, the time axis will stop being homogeneous which sort of ruins the effect of 'at-a-glance' time awareness. If there was a big block of down-time on the holiday, why do you want to mask it by covering the gap in the graph? The representation loses faithfulness that way. But maybe a faithful representation is not that desired here, hmm :-D