1.
Try to free up iPhone device storage see this Apple articles below:
If you need more space for an update on your iPhone, iPad, or iPod touch
If you need more space for an update on your iPhone, iPad, or iPod touch - Apple Support
How to check the storage on your iPhone, iPad and iPod touch
How to check the storage on your iPhone, iPad and iPod touch – Apple Support (UK)
Clear Other storage on your iPhone or iPad
Clear Other storage on your iPhone or iPad - Apple Support
2.
What's the difference between device storage and iCloud storage?
What's the difference between device storage and iCloud storage? - Apple Support
See this Apple article: Upgrade to iCloud+ -< Upgrade to iCloud+ - Apple Support
See also: iCloud+ plans and pricing -> iCloud+ plans and pricing - Apple Support
Manage your iCloud storage
Manage your iCloud storage - Apple Support
3.
and says I need an update in order to restore service
See these Apple articles below:
If you see No Service or Searching on your iPhone or iPad
If you see No Service, Searching, or SOS on your iPhone or iPad - Apple Support
Manually update your carrier settings on your iPhone or iPad
Manually update your carrier settings on your iPhone or iPad - Apple Support
Update your network provider settings manually on your iPhone or iPad
Update your network provider settings manually on your iPhone or iPad – Apple Support (UK)