Yes. iPod touch works seamlessly with AirPods. It supports the simple one-tap setup, and it will also set up automatically if you are signed in to iCloud and set up on another supported device.
Yes. The same MFi-certified controllers that you can use with iPhone, iPad or Apple TV also work with iPod touch. You can download hundreds of your favourite controller-supported games on the App Store.
1 Available space is less and varies due to many factors. A standard configuration uses approximately 10GB to 12GB of space (including iOS and pre-installed apps) depending on the model and settings. Pre-installed apps use about 4GB, and you can delete these apps and restore them.
* AirPods sold separately.