If I put my photos on iCloud, does free up space on my hard drive?

you can keep a reduced file sized version of your assets on iOS or OS X provided you are on iOS 11.x or OS X 10.13.x - so yes you can free up space using iCloud if your OS platform meets those specs.

https://www.apple.com/icloud/photos/

No. The photos are retained on your computer. Go to Photos/Preferences/iCloud and select Optimize. That will reduce the space required by about 90% when fully effective.