Why does Android OS consume my network transfer? The app data usage section of the Settings mentions that "Android OS" has taken transferred 1.73 MB of data in the background.

What is that caused by? I have disabled captive portal detection on my device. I'm running CM 13.0 without Play Services.
I've noticed on my CM13 phone, I will periodically get notifications when there are new nightlies out.  Have you tried disabling the automatic checks for updates?  Simply go to Settings->About phone->CyanogenMod updates->Check for updates-> Set to 'manual'.