Yesterday during the evening I went away and the computer didn't fall asleep. When I got back, I worked with it a bit and went to sleep. When I woke up, the computer was asleep. I have no idea what is the cause for the inconsistent between the 2 times (read more below).
Most of the times, the only thing that is working is edge, I disabled startup boost feature which I enabled not long time ago but the inconsistency continued.
1) I ran the following after the computer did go to sleep so obviously the output is when the correct behavior is performed.
Wake History Count - 1
Wake History 
Wake Source Count - 0
powercfg -devicequery wake_armed shows.
Intel(R) Ethernet Connection (2) I219-LM
HID Keyboard Device
Logicool HID-compliant Optical Wheel Mouse
Intel(R) I210 Gigabit Network Connection
2) Notice that the issue is not that something wakes it up, the problem is that something prevents it from sleeping in the first place. So I wonder if you are familiar with an application that tracks the sleeping timer of a computer. Something like showing a timer until sleep mode and if something happened that resets this timer, it shows it.
3) I noticed something interesting. yesterday (29.4) the computer didn't go to sleep and I see nothing from yesterday (29.4). Today the computer was asleep but it should have slept at around 2am (I went to sleep around midnight). Instead, only today (30.4) at 7:53am I see "The system is entering sleep. Sleep Reason: System Idle", meaning, ~8hours! after I left the computer it went to sleep. What happened during that time? I have no idea. The next entry is today (30.4) at 10:41 when I woke it up. So instead of sleeping most of the night, it actually slept only in the last 3 hours.
4) yes, it went to sleep when I manually set it to go to sleep
5) No, the network is always there.
6) not that I'm aware of, nothing is scheduled for the relevant times.