That sounds like the malicious third party program ban. Looking at your account history, it does look like someone hacked your account in November, 2017. There's a pretty clear change up in summoner spells and champions played. I'm far from fluent in German, so I can't read the conversation with Support, and my ipod is being a jerk and won't let me use my image translator app, so I'm going to have to come back to it in a bit, but the parts I can read are the 3PP bit. Which isn't too uncommon when an account is hacked. Someone may have stolen your account, and used it for a temporary boosting service, or even just to test out a new set of scripts.
It's very unfortunate when something like that happens. You should do like the others say, and submit a ticket to player support. They can assist you with recovering your account, and you can try to explain to them that you have not used any sort of hacks or scripts, and that you suspect they were used by the person who gained unauthorized access to your account. Support has many ways of telling whether it was the same player or a hacker who was in possession of the account during the use of the forbidden programs. As a rule, they are not going to tell you the specific way in which the hack/script was detected. That is simply policy, as Riot does not want to make it easier for actual hackers to discover how they were caught. So, it won't do you much good to ask them questions like "but what got my account banned?" They can't tell you that.
You should probably start with asking them if the hack occurred during the time frame that you were not playing. If they say yes, then that gives us a good place to start. What you can also ask them is if they can analyze the biometric pattern of mouse and keyboard clicks that occurred during the time when you know that you were in possession of the account and compare that to the time when you suspect someone had hacked your account (November/December 2017). The system does track that data, and they do have access to it. It's much more precise than something like an IP address check. By itself, all it would prove is that someone other than you was playing on your account. But, combine it with asking them to run an IP address check, ISP service provider check, and location of play check for that same time period (November/December 2017) - clarifying that you are NOT asking them to share the details of that with you. Ask them to compare that information against your own. If the locations, IP addresses and ISP are different, you've got even more support that the use of the malicious program was done by someone other than yourself.
If for some reason Support says that the hacking/scripting occurred prior to your taking a break from League, let us know, and I'll have an entirely different set of questions for you.
