Increase my storage in my phone

No, they are NOT safely stored anywhere else unless you sync them to a service like Google Photos, Dropbox, box.com, etc.

If you are thinking of iCloud, it is a sync service, not an archiving service. So if you delete a photo from your phone it will also be deleted from iCloud (and any other devices that share your iCloud account).

You can also download them to your computer using a USB cable.

Either you personally upload them "somewhere else" and wait until you see them there (or allow the other service to do so by itself), or even better, activate the "iPhone space optimization from Settings > Photos (this is assuming you have enough space on your iCloud account).

You need to sync your videos to your computer. You can delete photos selectively. Just don’t delete your videos.