If I back up everything on iCloud can I delete (what I already backed up) on my iPhone?

What do you mean when you say you "have them backed up on iCoud right now"? Are you using iCloud Photo Library? If you are, then you cannot delete photos from your phone or they will be deleted from iCloud. If you mean that you back up your device to iCloud, that is not savings your photos permanently.

If you want to save your photos you need to import them to a computer using the photos program that comes with that computer:

PHOTO IMPORT IOS TO MAC/PC

Once you have imported your photos to your computer, you should then back those photos on the computer up regularly. If you are using a Mac, you can di that by using Time Machine backups on a regular basis.

Your device, nor the backups you save for your device are a safe place to keep photos that are important to you. Backups are not photo archives. They are backups of your entire iPhone contents, which includes the photos you have a the moment you back up, but each backup, in essence, replaces the last one. So, if you backed up, then deleted a bunch of photos, then backup up again, the photos that you deleted would not be able to be retrieved.

Import your photos. Import them regularly. And then back them up. Otherwise, you will encounter a situation where you lose them forever.

Best of luck,

GB

Back up is really not the best word to use what you are describing here, as it is easily confused with actual backups which are done to iTunes and iCloud, but which have nothing to do with getting your photos, specifically, to a safe place. Import is the term that I think you were intending here, and it is always beset to make that distinction. Too many users think that a simple iCloud or iTunes backup is going to save their photos....

Cheers,

GB

If you want to save images - back them up to your Mac in iPhoto or Photos

The Photo stream and iCloud Photo library are transitory

Backing up the pictures to your Mac makes it a little more permanent - however if they are images you absolutely need to preserve I would do one more back up like OneDrive or Carbonite

You are correct - which is why I gave OP other alternatives including backing up the backup using a continuous cloud service like Carbonite.