how do i know that the photos on my mac are in icloud? and can i delete photos from my mac to have space on my desk?

Answering your second question first, you should not delete photos from your Mac. If you do, those photos will also be deleted from your iCloud Photos library in the cloud (and from any other Apple devices linked to the same cloud library). That is the purpose of iCloud Photos: to keep all of the link libraries synced.

What you can do is enable "Optimize Mac Storage" in Photos on your Mac. While it is enabled, a storage shortage on your Mac will trigger the reduction of some photos to lower resolution, down to mere thumbnails if needed. When you need the full-resolution version of a photo (as for printing or editing), it will be downloaded.

Your photos should be in the cloud when the status displayed at the bottom of the All Photos view is "Updated Just Now" instead of some variant of "Uploading". You can double check by going to iCloud.com in a browser, logging in with your Apple ID, selecting the Photos view there, and reviewing the photos stored there.