Good evening! What does these messages mean? And is it official from Apple?
iPhone 6s, iOS 14
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1.
For that message: see this Apple article ☞ If you can’t turn on or sign in to iMessage or FaceTime
https://support.apple.com/en-us/HT201422
Perhaps Is your Wi-Fi network Is unavailable?
Turn on Wi-Fi network: Settings ☞ tap on Wi-Fi ☞ turn Wi-Fi ON
2.
The range of the mobile network is minimal. Do not wait until 'No service' appear.
See this Apple article:
If you see No Service or Searching on your iPhone or iPad
https://support.apple.com/en-us/HT201415
3.
Low Power Mode is On.
Charge the iPhone.
Wait until the battery is fully charged (100%).
The Low Power Mode will turned off automatically.