Can I recover my photos from iCloud backup?

You should recover the photos that were in the camera roll when your phone was backed up.

Restoring to an iCloud backup has to be done in the initial device setup process. If you have any newer data on your phone now that is not in the backup that you want to save you'll need to do that first. When you're done, go to Settings>General>Reset and tap Erase All Content and Settings. Then go through the setup screens on your phone and when given the option, choose Restore from iCloud Backup. Be sure it is connected to wifi and your charger as this will take some time to finish.

Anyway to restore photos from Mac to iPhone through iCloud without deleting and going back to inital settings?

No. Not from an icloud backup.

But, since users are usually advised to sync photos to a computer to archive them, if you've been doing that, then use iphoto or aperture (whichever currently has copies of the photos) to sync them back to the device. This does not involve icloud.

If you didn't back them up, and you didn't upload them to PhotoStream or some other online photo repository, you don't. They are gone.

If you've previously synced the pictures to a computer (as is generally advised to archive them), then they are gone, unless you have backed up the device to itunes or icloud. If so, you need to perform a restore:

http://support.apple.com/kb/HT1766?viewlocale=en_US&locale=en_US

Go to Settings>General>Reset and tap Erase All Content and Settings. This will erase your phone. Then you will go through the setup screens again as you did when your phone is new, and when given the option, select Restore from iCloud Backup.

Note that you cannot restore just one file, it's all or nothing.