Can I buy more iPhone storage?

Incorrect. iCloud does not offer independent archival storage for photos, videos etc. it is a synchronization service, not independent storage. Photos in iCloud will always also need to be on your device. If you delete them from your device, you delete them from iCloud.

Even if using iCloud backups for photos, each new backup will end up overwriting the previous backup. So you will loose information that way too over time.

The only way to truly secure data and delete it from the device is to copy it first to some independent archival storage, like a laptop or desktop, external drive, or archival online storage service (e.g. Dropbox, Box).

No.

You can not increase the internal storage on the phone.

The best option is probably additional icloud storage. For a monthly fee you can backup photos, files, texts, etc., to the cloud and then remove them from your device.

Hope this helps!

That is incorrect Zach, iCloud does not work like Dropbox or OneDrive, it is a syncing medium. If you move photos to iCloud and then delete them from the iPhone it will also delete them from iCloud.