Your requirement is to create an automation tool for testing. It's similar to TestArchitect, Test Complete, Quick Test Pro, Selenium.
1- For Chrome Desktop, your requirement can be served by creating a plugin using NPAPI to do ICP communication and javascript invoking. But it seems Google will deprecate NPAPI by end of this year, later Chrome version. for now we have many alternatives to do IPC. But I'm thinking of a more stable approach using wekit proxy.
2 - For Android. the solution depends on your detail requirement. If you want to support third party Android brower such as Dolphin, It sould be implemented using Instrumentationation to inject our code into Android app and using javascript to get information from WebView. If you want to support Chrome or other built-in browser. It should be implemented using Webkit proxy.
3 - Selenium and Appium are famous but for Selenium, it's hard to use in large-scale testing project. For Appium It's hard to configurate and easy to crash (I faced many times).
I'm senior developer with 4 years in making automation testing framework mobile UI testing: Android, iOS, Chrome, java, dotNET, Win32.
My bid is 20 days but It depends on your detail requirement. It may take a longer or shorter period of time. I hope we will have chance to work together.
thanks.