Are these bugs, cheating or what?

I happened to be allied to both conflicting sides. How is it possible that those sides can occupy my towns, however I can't attack them and yet they can move through my defense lines. Yet another thing with the same player (who occupied my cities being an ally): how is it possible to take 8-militia neutral city and lose only two tanks (in this case 4 infantry, 4 tanks vs 8 militia = 2 tank loss)? I have suspicions of cheating.

Firstly, were your cities empty? If so, then yes, both your allies can take your empty cities. I suggest leaving 1 unit in every city if you don't know if you can trust your ally.
Second thing - he managed to get extremely good rolls, that's why.

You can move through walls of players you have alliance or peace with. You can take yours ally cities if they leave 0 units in the city (probably what you left your cities empty). If this player uses a strategy that focuses on tanks it's not unusual, if he uses other strategy with a little bit of luck it can be done.

Ty, didn't know i can't leave my cities empty. It wasn't written in the faq. Another question can marines move through the walls unnoticed?

If they are allied, they can.

I suspect the following reason for the ability to take 0-unit-allied town, because he is your ally, it may come to a situation that you want to give him any town(s) on free or trade with other cities or cash. But some backstabbers misuse it. I was cheated once when I was noob.