How do I save my photos and videos to my phone too instead of just iCloud library?

When I don't have good cell phone service and I try to play one of my videos I took from my library it won't work. How can I fix this so they can always be played from my iPhone no matter what?

The biggest problem you'll be running into, or already have, is storage capacity. While cloud storage is virtually endless, at least as long as you pay for it, local storages on phones and computers is limited. Storing a selection of your photos and videos on different memory cards may be a temporary solution, but these things are small and easy to lose.