Can deleting zip files harm your computer?

No. There is no problem in deleting zip files. They are just left behind after file downloads.

.zip files are compressed archives, containing 1 or more files. Deleting a .zip file will not harm your computer, as they are not system files. If you delete a .zip file, all you will lose is the files contained within. If you have already extracted the files, or if you no longer need them, they are perfectly safe to delete.