For that, you can download the “Everything Installer” from https://alt.fedoraproject.org/ - that’s a smaller download and doesn’t include the live boot.
In Windows you could try these steps to remove the locked partition from the USB stick.
Regarding the media check failure, you could follow this guide and see if that sheds light on the problem. Although there’s a good chance the USB stick had a pre-existing hardware problem, and it would be worth trying another one.