Particularly, where can I browse the source code for any android source application(e.g.the contact application) ? Is the only way to go to download all there is?
Contacts is here for example.
Android official source browser (based on Gitiles) has a web view of many of the different parts that make up android. Some of the projects (such as Kernel) have been removed and it now only points you to clonable git repositories.
To get all the code locally, you can use the repo helper program, or you can just clone individual repositories.
You can view the source code through http://developer.android.com, when you're reading the API there will be a link to the matching source code on GitHub, you just need to add the Android SDK Reference Search Plugin on Chrome.
I blogged about it here: