After my brother deleted some system files from my Macbook Air I can’t reinstall macOS
This is a pretty rare failure since the installers are signed. You would want to review a couple things:


https://support.apple.com/en-us/HT204904


If you have a backup - consider using Disk Utility to erase the internal drive - then the installer would have less work to do. - https://support.apple.com/en-us/HT208496
Consider your network - are you behind a proxy / firewall / or located a distance away from the main servers in US? Taking your mac to a new network might fix everything without needing to erase things.
Shut down any caching servers that are local to your network. This might be hard to figure out if you aren’t the network admin or don’t have a mac. If you have another Mac running - run the command AssetCacheLocatorUtil



In the end - your computer couldn’t get a good image to start the install. This is almost always a network / server issue, but you might be able to fix it moving to a new network, validating the date/time on your Mac before you install the OS or changing the version of OS you request.