So, if I am regularly backing up to iCloud, may I delete all of the photos and videos from my phone without losing them entirely?

If you have important photos you should have multiple independent backups. First, as muguy noted iCloud is NOT an archiving service, it is a syncing service, so it is useful for transferring photos to other devices such as a Mac, iPad or Windows PC if you have iCloud for Windows. Once the photos are on another device you can export them to folders on your computer drive.

There are several excellent archiving services that work with iOS devices: Google Photos, Dropbox, box.com, Shutterfly, Amazon Photos, Microsoft OneDrive, Livedrive and others. Some also offer sharing and organizing features, including Google Photos and Shutterfly.

I sync photos to iCloud, but also export them to the Pictures folder on my Mac, where I also store photos taken with my other cameras. Google Photos picks up all of those as well as my iPhone photos. I also back up photos to Livedrive and Dropbox.

Hello ~ I use a quick easy little device called an iXpand. I also export them to another service.

~Katana-San~

That depends on your end goal. The easiest way is to sync with your computer and then put them somewhere (external drive, disc, etc.) and also make a backup.

You can also sync through iCloud and enable optimize photos to reduce the size of photos on your device (in some cases by up to 90 percent).

No. iCloud backups are incremental; changes are made to the backup based on your device changes.

If you sync with iCloud, deleting images on the device will also delete in the cloud.