iPhone 7 there is no connectivity to cellular
Try first to optimize the range of the mobile network, see this Apple article:
If you see No Service or Searching on your iPhone or iPad
If you see No Service or Searching on your iPhone or iPad - Apple Support
After you have optimize the range of the mobile network & the iPhone stll ’searching’, see ->
iPhone 7 Repair Program for "No Service" Issues
iPhone 7 Repair Program for "No Service" Issues - Apple Support
The most recent download was held up because I did not have enough space.
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
What's the difference between device storage and iCloud storage?
What's the difference between device storage and iCloud storage? - Apple Support
Still I have no inbound telephone nor outbound.
See this Apple article: If you can't make or receive calls on your iPhone
If you can't make or receive calls on your iPhone - Apple Support