I thought that was strange, I used most of these apps before on older devices, why does everything no longer work on a device that's relatively new? According to those error messages the device is basically useful, it can't install apps any more, which is the heart of the ipod touch.
I searched around online and there's an official solution. I had to install itunes on a computer and login to the same account as the Apple account on the device. Then I had to download the incorrect iOS 7 version of the free app I wanted. That would assign it as a purchase to the Apple account. Then I could delete that download. Then, I had to open up the Apple store on the device like I was doing previously, find the free app on there again, and click download. After doing all that, it wouldn't give an error saying the device wasn't supported, but now ask if I wanted to install the last compatible version.
My mind was blown. How could such popular software provide such an awful user experience? The ipod touch said the app isn't supported for the device, but then I 'buy' the free app on itunes, and magically it is supported and I can download a compatible release.