Reinstalling MacOS Issue

See the section 'If you can't start up from macOS Recovery' in the link below.

https://support.apple.com/en-us/HT201314

Hope it helps.

As you have an Air it is probably not possible to connect to your router via cable, the preferred method.

If you have to use WiFi move your mac as close to your router as possible. If there are any other devices

that share the same internet connection please do not use them while the mac is downloading from

the Apple Recovery Servers.