PHP is a scripting language that usually powers the backend of a website, and JSON is a format used to transmit data between servers. I don't think either of those have anything to do with Android development. I do know, however, that you are trying to use our API, so maybe some others could point you in the best direction towards integrating our API into an Android app.
You can use sites like PhoneGap to convert CSS, HTML and JS to native apps. I've yet to see a conversion site that can convert PHP code to Java (native Android) or ObjectiveC (Apple) in this context.
You could develop a "front-end" which connects to a remote host which can deal with your php/mysql stuff via ajax (js). However, if you're dealing with the DW API, you can use "just js" (Implicit Flow), which may obviate the need for any server-side code, thus allowing you to use sites like PhoneGap.
I've tried many of these types of sites and the best involve using node.js This is great for those already up to their necks in it. Bit of a learning curve for those not so hot on it. The code samples on a lot of these sites can be problematic too. Inasmuch as they don't work! Take time to check them out, perhaps you'll be luckier than me.
You will probably need to download an SDK for each platform (and possibly each device). That's fun too :(
Some sites provide a plugin for Eclipse. I tried these with varying degrees of failure. heh heh.
Android Apps are pretty much written in JAVA compiled in android SDK. The only thing that the PHP can help achieving the mobile apps is to provide the API in the form of RSS or XML. Even so, XML and RSS are not always a good source of data. What I have seen in the past was a complete parsing of the URL and the harvested data are then translated into the JAVA compliant xml file.
There is an rss feed reader on github of which I believe can help you start with this project. The script will read any rss feed from daniweb.
You can pretty much make this work by downloading the Android SDK or the Android STudio and then just import the source codes from the linked git hub source codes above.