Is it possible to change the buttons, analog sticks on the controller?

I'm sure that if you have an issue with the controller itself, you could request parts from the manufacturer. As far as switching out parts, it may be possible for some parts of the controller to be switched out with other similar ones, but it may require significant manual modification of the part.

With the recent software updates of the OUYA you can actually hardwire a 360 controller via USB or Bluetooth a PS3 controller to the OUYA

Yes and no, So lets start with the yes, the analog or the thumb sticks, there are almost a dead on size of the Xbox 360 controller thumb sticks, 360 fit prefit and they are way cheep, here is a link where you can buy multiple colors and also metal ones if you like. http://www.ebay.com/bhp/xbox-360-analog-...

Also here's a video to show you how to replace them. https://www.youtube.com/watch?v=FVtBPAif...

Good luck and have fun, love the Ouya

You will need to use 9mm Xbox 360 thumbsticks to take up the gap on the Ouya controller, here's the link to the place that sells the products that you will need , Good luck. https://modsticks.com