The vibration and/or beep signal the beginning of a human turn. I intended this to alert you to pass the phone to someone else if you're playing with friends. These can be controlled based on your android settings ("Audible selection" and "Haptic feedback" under "Sound settings.") I'll add an option to override those in the application.
I have a new version (almost ready) that adds a bunch of minor features, including a turn log as you suggested. It also lets you set player names and colors, and have a combination of human and ai players.
I have a buddy working on some new textures. Saying he's a better artist than me is an understatement. See screenshot above
I have a short list of bugs to fix and some things that came up in testing. I'll have another release out within a day or so.