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iCloud does back your entire iPhone and iPad as well as backup Documents, Contacts, Calendar in separate location. You don't need to do individual back up like email. To do full backup, go to Settings > your account > iCloud > Backup and you can do backup there.
You can find what items are syncing to iCloud from Settings > your account > iCloud (or Settings > iCloud)
To find out what is stored on iCloud, you have to check it from a computer. On your computer, go to www.icloud.com
Login to your iCloud account and you will have access to all synced information there.
If you would like to backup your entire Photos app, then go to Settings > your account > iCloud > Photos and enable iCloud Photo Library.
To buy more storage or upgrade your storage plan, then you can do that from Settings > your account > iCloud > Storage or iCloud Storage. You will be able to upgrade iCloud Storage there.
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