is macOS Catalina free?

macOS upgrade have been no-charge since OS 10.9 Mavericks''

Also, when i come to download mojave it is saying that it is damaged can anyone confirm why?

That message usually indicates that you have an older and out-of-date version of the installer already in your Applications folder. Find it and delete it. the thry again.

NOTE: There are many reports here that Apple system downloads are not working with FireFox. Use Safari to download the current version of the installer

It's a free upgrade.

The reason you're seeing the error you are is because you have an old version of the installer downloaded.

You need to delete it, reboot your Mac, then re-download it.