Christophe,
We have done some specific work around downloading all assets on the iOS side of things, so it is definitely possible.
I think utilizing something like Cordova/Ionic would meet your needs for getting something up and running quickly. You might be able to sue the existing web app code and modify it to download all content.
For stats I would just utilize Google Analytics, you may need to setup some form of caching of the data though if there is no connection. There are other tools like Flurry that might also work well for this.
If you have a solid Android dev, I would think the basic functionality of TAP would not be too hard to build for android as well. We just have not had the proper resource to do it ourselves.
Kyle