Going to try to address your issues sequentially. First, the app doesn’t open because it’s code is on a web server. It is possible within a webapp to build a manifest list and force the phone to cache the code however the HTML files contain dynamic PHP code thus caching is somewhat difficult.
As it stands, the OpenSprinkler does not log anything. My mobile app (the PHP version) polls the OpenSprinkler every minute and logs changes. When you open View Logs, that log is parsed for the selected date range and values are returned. This means the data is not interpreted but rather actual logged data. The data is therefore stored with the html/php files such as config.php (SprinklerChanges.txt). The watcher script can be found here: https://github.com/salbahra/OpenSprinkler-Controller/blob/master/watcher.php. The installer attempts to add the script to crontab otherwise alerts you it couldn’t.
Which import button are you referring to because that is only used for the configuration. If the device is down what good what that do? Just curious here.
The OpenSprinkler HTTP API is documented here: http://rayshobby.net/wordpress/wp-content/uploads/2011/10/Firmware1.8HTTPGETcommands.pdf. With a few exceptions of course.
The following new options are available since 1.8:
o2 – NTP On/Off
o14 – Auto Reconnect On/Off
o26 – Device ID (0-255)
Hope this clears up some of the confusion.