So is the first problem is fixed? Now it is only the batch settings you are asking about?

If you restart Photoshop then the batch settings will need reselected. However, if you haven’t restarted Photoshop, then the batch settings window should retain the settings. In the fututre, I would like to program it to remember what settings it can make it remember on a restart but I haven’t programmed it to do that yet. There will be no way for it to remember file or folders settings on a restart though. This is a limitation on the new plugins API for file and folder security implements by Adobe.