Hi,
1) I totally agree with this one (Happened to me as well) this is one of the things you neglect since it's so small, I've added this to the issue tracker and I'll add this soon.
2) I'll add the save last folder to the next release, as for the drag drop, you can currently import files/folders by dropping them into the main application window (duplicates are ignored),
3) You can create the photo index anywhere you want, by either moving the index file to an other location and using the File-> Open menu or create a new photo index with the same menu which is useful when you have a large amount of photos, the thumbnail cache file is created for each index file.
The thumbnails cache file can also be moved by using the cache settings menu
Asaf.