PNG Compressor works great. http://www.shpakovski.com/png-compressor/

Some inspiration: http://www.androidux.com/Onboarding-Tipshttp://www.pttrns.com/categories/16-walkthroughs

For some people this may help, or Paper Prototyping at all. For me, it is not an option. After some hand-drawn rough wireframes I fire up Axure and build that stuff within minutes and can test on the real device.

For the Icons itself I extract them and create separate artboards for each and use the following settings: https://twitter.com/martinthiemann/status/535082123976531968

For specification, maybe have a look at https://zeplin.io

Regarding 3) You have to think about displaying a loading spinner/indicator, since the app will be slower than a native app and you do not have the loading indicator from the browser.