Hello,

I'm EU citizen and will get next days my first permit in Ch-Bern, I do not have another domizil somewhere else.

I'm driving a car which is registered to an EU company, owned by a friend of me. I have with company nothing to do. My job in CH has also nothing to do with this company. Of course the car has green card valid for CH and technical inspection too.
So, I think, the car could be considered as a long-term rent or lease? Even if the car is quite old

How long can I drive this car in Switzerland (with EU plates)?
Can I register this car as household, even it's not mine, according to the current papers? Basically I have older papers, which proof the car was mine some years ago

You are not allowed to drive that car inside Switzerland as of the moment you become a resident here unless you import it or arrange an official exception (Don't see in this case how you can arrange an exception tho)

Also you can not bring it in the country free of fees/taxes since you did not own it the last 6 months before moving, now if you could proof you are the main user (as is the case with for example lease constructions) exceptions can be made, but in your case it is registered to a company with whom you I assume have no contracts or anything (Ain't that fraude in the country you currently are in?)

Not even close unless the company is in the business of leasing cars and it has all the necessary paper work to lease it to a Swiss resident.

Up until the first time you are controlled and then it will be a question of how much it will cost you - expect it will be painful.

I won't even ask how that happened because it is sounds doggy to say the least. But no you can't do this.

If it's a company car it can be arranged to import it under the 6mo rule for free.

The company has to provide some evidence that you are connected to it, and that the car was provided to you as part of that connection.

If it's a friend and you had nothing to do with it, I don't think you can do it, so don't try to f* with the authorities because it can get extremely expensive.

I'd suggest you get a cheap car in CH, there's lots around.