You asked for a link to get the source code. A good starting place would be http://source.android.com/
It's both a product and a service, it just depends how you define those terms.
Product - a product can be defined as "a thing produced by labor", it is. A "thing produced by or resulting from a process", Android was developed with various processes. Also check the third definition and you'll see the overlap with services, "the totality of goods or services that a company makes available".
Service - "an act of helpful activity", well they helped the mobile OS community. "the supplying or supplier of utilities or commodities" - stuff like the Market, GMail, etc may come under this.