So if I put photos in my iCloud drive, does that mean I can remove them from my computer to free up storage space?

No.

You can allow iCloud to manage your local photos storage.

iCloud Photos does host your photos on Apple’s servers, and you can let iCloud manage how your photos are cached on your iPhone…

But… if you delete a photo locally (when iCloud Photos is enabled), it will be deleted everywhere.

See the optimize-storage info here: Manage your photo and video storage - Apple Support

There really isn’t a great way to work around a lack of local storage on an under-configured iPhone or iPad. Some offloading is possible (and iCloud and iCloud Photos can help there), but can require ongoing storage management.

Not necessarily. If you use iCloud photos on your Mac, it will keep your photos in sync with those in the cloud. You could upload all of your pictures and then disable iCloud photos. If disabled, you could then delete all the pictures on your Mac and they will live only in the cloud. Of course, then you have no additional backup copies.