By default Airplane mode disables all wireless frequencies on your device so that you can comply with airline regulations. This means that any radio frequencies relating to cellular, Wi-Fi and Bluetooth are disabled.
However, when your device is in Airplane mode, it is actually possible to manually enable Wi-Fi and/or Bluetooth. And, if you do, the next ...
Leave it alone, it will get there.
If it's claiming such astronomical time remaining, it's based on 'how fast it went so far vs how long it thought it should have taken'. That's a variable dependant on many things - HD vs SSD, space remaining on drive etc.
Also, your download speed will have an effect - maybe significant if your ...
Your question does miss some key details, so this answer makes the following assumptions:
You've correctly identified your current Boot ROM version
Your MBP still has the original Apple SSD installed
You've already tried (directly or indirectly) resetting the NVRAM
You've never installed macOS High Sierra on your MacBook Pro
Essentially, some years back ...
You might need to check the boxes "Check for updates" and "Automatically download updates when available" for the download. Also, Check firewall options for allowing connections if denied.
https://forums.macrumors.com/threads/where-are-downloaded-software-updates-stored.1629444/ and as I too verified, updates are located in Library/Updates before install. ...
You downloaded the 'delta' Update file from Mojave 10.14.2 to 10.14.3, not the full upgrade installer.
You can only get the full installer through the App Store, & only if your machine can run Mojave.
If your machine cannot run Mojave, then see How can I download an older version of OS X/macOS? for suggestions.
lsof doesn't always show the root processes running. So sudo to be used.
sudo lsof -p PID | grep TCP
PID to be replaced with the PID(Activity Monitor is one source.). TCP can be replaced with other protocols too. For unfiltered results removed the | grep TCP part.
For anyone who still struggles with this, if you have more than one user run on your Mac.
Open /Users in the Finder and right-click > Get Info.
Change permission settings to Read & Write. (If you have 3 users then change all 3)
Setting Icon > Apply to enclosed items
Redo answer from Lounès KSOURI. (Or just check the software update again)