Once my airport time capsule has backed up my files, can I delete them from my hard drive to free space?

No, No, NOOOOOOO!

In some weeks, maybe months, TimeMachine, will purge those files from the backup, because they no longer exist on your Mac.

If you need an archive, use separate external storage. And if those files are important to you, make sure they get backed up as well. The external storage could be an external disk, an home NAS, such as Synology, or cloud storage.

But DO NOT use TimeMachine and also delete them from your Mac.

I guess you could but I would not recommend you to do so. If your Time Capsule fails, you’ll have no way to recover your files.

When it comes to backups, this is the recommended rule: https://www.backblaze.com/blog/the-3-2-1-backup-strategy/.

At the very least, have two copies of your files at all times. You could get an external drive to offload some of your files. Then you’d have the Time Capsule and the external drive storing at least two copies of your files.

To confirm, no, deleting a file from your Mac won't remove it from your Time Capsule backups.