Screen Mirroring with Chromecast
The original Nexus 7 does support screen mirroring to Chromecast. This feature was added in Android 4.4, so if you're still using an old Android version on your Nexus 7, you'll need to do a system update. From the Settings app, go to Display then Cast screen. Don't bother with the Chromecast app at all.

The option's in a different place on the S3, and it's designed primarily for Samsung's competitor to the Chromecast, but I expect it would work with both. From the Settings app, at the bottom of the Connections page, click Screen Mirroring. The phone will start looking for devices it can cast to.