Ok, we have had some progress with the standalone tables but are still having some issues:
First, I tried to create a dummy point which had same coordinates, for each row. What happened was that when I generated the points for one feature class and created mobile cache, it had features. When I added another feature class to the map, generated the points (same coordinates as previously) and created mobile cache, there was no features anymore in the mobile cache... If I removed the another feature class from the map and created the cache again, it worked.
Next thing, I had one feature class on the map, and then I added another one, for which I generated points with different coordinates than the first feature class had. It worked! The script I use for creating those points generates now randomized points.
Ok, so randomized points are fine because we know which tables contains the dummy geometries. But there is still a problem because there seems to be some kind of a limitation how many rows we can add to each feature class. For example, we have a table which has 14 000 rows, if I add all that data to feature class, generate geometries and create mobile cache, it's empty. I have tested to remove all but first 5 000 rows, and it works. Geometries are fine in ArcMap and all data is shown when I browse that feature class, so it's something that happens in mobile cache creation. Has anyone had similar problems or have any ideas how to start debugging this?