iPhone Storage

You cannot purchase more internal memory/storage, the buck stops at 16 Gb, you will need to delete data off your phone to gain it back. How to check the storage on your iPhone, iPad, and iPod touch - Apple Support

You purchase more icloud storage to either backup or sync data to icloud.

Once you back them up to icloud, and delete it off your phone, the next time you backup, it will override the previous backup, so those pic will be gone.

It backs up data that is currently residing on the phone.

No.

You can save your photos into your computer.

Not necessary, I would look into google photos, to do what you want.