I AM a nice and knowing guy

As far as I know, they did't play at the time I was banned. I don't know if they even use Ambrosia servers.
As for the tut, I tired that but got stuck pretty much at the beginning

and concluded that is not for us mortals, but only admins with another software or whatever..

I'll give it another try...

I had trouble finding the path "steamapps\common\Counter-Strike Source\cstrike" because "steamaps" folder doesn't exist in my CS folder... I accidentally saw another .dem file and then copied the file downloaded from here to that folder and then managed to play the demo.
I've watched it, only once, unfortunately, when I tried to replay it, the message said "error".. My impression, with all those lines flying around I look pretty awesome

I saw those lines once in a video on YouTube, but have no idea about what I should do to "install" them. I honestly don't.
I am an honest guy, and after seeing the demo, I admit that some situations look suspicious even to me, but that is pure coincidence, I swear I don't use cheats, and NEVER have used. The fourth round presents the situation I described earlier, you see how one thew a bomb, and the other one came from the alley, as I described. And I was waiting for quite some time, even hid behind the wall, but maintained my cross in front of the tunnel. If there was another player instead of the one I killed with a bomb, damage, for example, it would have been the other way around, he would own me. He always does!
And in one of the fist three rounds, I think, there is a situation when I am a few meters away from the tunnel, approaching from B, the green squares are clearly still somewhere at T base, and I glance at that small "tunnel" where you have to crouch in order to pass to the other side... You know what I mean... My point is, if I did use wallhack, I would see all those lines and squares, right? Why on earth would I then bother to look to that "tunnel" if I already knew no one was there?
Also, there is a situation when I hide in a corner behind a wall in front of B, although there is no one behind me (there are no lines or squares), they (or he, I am not sure) stay far behind... Again, why would I hide if I KNEW no one was after me???

In continuation of the same situation, after that "hide and seek" I start moving towards A, and after I emerge from behind the wall and have a look at the area in front of me, I kill the guy approaching from the other direction, I see him first, I start backing up and shooting, and kill him. I didn't "SEE" the lines and move purposefully towards him, it was pure luck to do that, and I killed him because I saw him first, started shooting first, and that's it. I can't remember if he even fired a single bullet.
I will try to play the demo again, and try to remember more evidence to my defense

If you look at those situations again, you will see I am right when I say I have not used cheats! I would be a complete idiot if did use wallhack and still perform those actions (hiding and running from myself, or looking in the direction opposite from the squares and lines). And I am not an idiot

Let me know what you think, and please try to find the date when "NEMOJ MENE

" appears on Ambrosia for the first time so we can at least solve one problem... I am from Serbia, I really don't know if the situation with IPs is the same here.
P.S. Could this be also the case with my IP? "A hacker's IP range was the same as yours. Probably someone in your neighborhood got range banned, so did you."