This app was mentioned in 7 comments, with an average of 2.14 upvotes
There is an app for android which is extremely good, and the developer still works on it and listens to the feedback: https://play.google.com/store/apps/details?id=nl.tengen.gridmaster&hl=en
The bot it ships with is at around 2k-1d KGS level or so, it knows plenty of joseki (can't beat it by messing with his opening) and it plays good games.
For your questions: I think GnuGo is very weak right now and obviously CS is better, I've been playing against CS on PC and it's a very good app + bot. I prefer CS between these two for sure.
This one for sure: https://play.google.com/store/apps/details?id=nl.tengen.gridmaster&hl=en
It's a full featured SGF editor, so just open a blank board, set it to "human vs human" (or something like that) and begin placing stones as if it was a real game. If you want a bit more comfort for the touch screen, you can subscribe to the beta releases and get the double-tap function (like cosumi has), unless it was already shipped to the release version.
You can also save the SGFs to then upload to your PC for reviews and other stuff. Or you can review directly in the app itself, though I'd say the latter is a bit less comfortable.
Try Go Gridmaster by Erik van der Werf. A neat little app that is hugely customizable, and comes with his own Go Engine called Steenvreter. The app also allows external engines to be installed (e.g. GnuGo, Amigo, Pachi). The free version is ad supported but fully functional (I have never seen any ad btw LOL)
https://play.google.com/store/apps/details?id=nl.tengen.gridmaster
If you're a beginner (first 50 games) that app is fine, the UI is very nice. The strongest and more accurate one around would probably be GridMaster , there are many other ones around (like GOdroid) i don't know which one I'd recommend.