No one here will tell you how they detect bots because no one here knows. I am reasonably certain that not even my CMs (people in charge of the forum) or the Support agents know. I suspect they have some software that check that for them, but the inner workings of that software are known only to the devs. So, for all intents and purposes, a black box.

As for your question, "how its phisically possible to send 50 attacks from 50 different islands within 1 minute by human?", it can be 50 well coordinated human accounts. It's actually not hard at all, if you have players that are very active and responsive. "All hit these coords at hh:mm:ss". They all send, use charts to get the right time, bam! Simple.

Note that I am not saying that this has actually happened. Only how it could be done, which is what you asked.

Whether it did or there is something shady here, I have no way of knowing.

that is the whole point, support does not tell anything and do what they please, without providing any edidence

They're not supposed to provide evidence. I don't like it, but I do think it's for the best. If they provided evidence, those who cheat would know how they were detect it and it'd be easier for them to circumvent these checks in the future.

This is quite standard, really. All games that I've played had the same anti-cheating policy.

excuse me but, are we suppose to just believe what they say blind eyed

evidence is part of any investigation and action

that makes no sense ....

i

There's only one thing to say here: it's beautiful when everything is destroyed in a minute. 

dududufdufduf duf

Yes, we are. You're not asking to see the game's code to check that the battles are performed the way they should be, are you? You're trusting them to have done their job. Same with this.

As for the "evidence is part of any investigation and action": yes, it is, and I believe that they don't just casually ban people because they are bored or something.

But sharing that evidence with you is not a part of an investigation. Plarium is not a public court of law. It's a private company whose terms and conditions  you have accepted when you started playing their game:

6. TERM AND TERMINATION

(c) Termination by us. We reserve the right to terminate or suspend your Account or access to any or all of the Games or Services at any time and for any reason. Where required by law we will provide you with prior reasonable notice. It is within our sole discretion and determination to terminate your Account for what we deem to be a violation or breach of these Terms or any Applicable Law. [...]

I repeat what I said before: I don't like it, but I see the reasoning behind it.

Also, it's kinda pointless to protest, since neither of us can do anything about it, except go play some game that serves its punished cheaters with hints how to circumvent detection in the future. IMO, good luck finding such a game, but maybe I'm wrong.

A god-given moderator. "We can't do anything, find another game." 

i

Crowbar, I am NOT protesting. 

What I am saying is, I provided clear evidence that my troops that I paid for to Plarium to build, were destroyed by someone using game managers which are illegal. 

Now, when I requested my troops to be re-instated because they were demolished using illegal software, I was told it was legal and everything is perfect.

Do you see the problem HERE? 

I see the problem, yes. However, you said above that you want the evidence, but their decision is actually a lack of evidence. You claim that the attackers cheated, Plarium (claimes to have) checked, and they (clame to) have found no evidence of wrongdoing.

The simple truth is that it is Plarium's discretionary decision. I sympathise with you and I even agree that it looks suspicius (while I disagree that the cheating is the only possible explanation), but my agreement or disagreement is irrelevant here. I can try to explain things, but no one on the forum can actually override Support's decision. Even the Plarium employees that run the forum have no say in the matter. To the best of my knowledge, it's on the Support, and only on them.

There is one simple solution to the problem 

i

I am posting it here not for someone's sympathy.

It is to warn people NOT to spend money, on such games. Because there are no rules, support overrides everything. They are the ultimate Gods.