Understanding Bitcoin Can someone maybe help me to understand the idea behind Bitcoin, because I really don't get it.

What I understand is the idea of mining, that there is the chain where each transaction is added to and it is decentralized which means that everyone is able to run his own instance of the chain (so no government or company can controll it completely).

But lets say I own one Bitcoin (an hash). What stops me to sell this one on different chain instances? As long as I understand, they are decentralized and dont have to synchronised at each transaction. Maybe they will find out when they synchronise at one point, but then it is to late.

Also the chain become bigger and bigger as more people start to make Bitcoin transactions. At the moment the chain has just a few GB as far as I know, but in the future it will have petabytes or more...and at this point still companies like Google or governments can store it, which destroy the idea in the first place.
You seem to understand the concept of decentralization, but also seem to be struggling with the concept of consensus.


  But lets say I own one Bitcoin (an hash). What stops me to sell this one on different chain instances? As long as I understand, they are decentralized and dont have to synchronised at each transaction.


What you are missing is that all the decentralized chains are really the same chain.  For the most part, there are no "different chain instances".  Yes, there can be a fork, where half the network thinks block A is the tip of the chain, and half think that block B is the tip.  However, this almost always gets resolved when the next block is found.  It is very difficult to pull off a double spend, and virtually impossible if the recipient is being cautious.  Most merchants/exchanges will wait for at least a single confirmation, often times more for larger value transactions.  Even before a single confirmation, double spends are very difficult.

Bitcoin is more than just a protocol for decentralizing a ledger.  More importantly, it is a protocol for coming to consensus on the state of that ledger, even when the participating nodes do not trust one another.  It is this ability to come to trustless consensus without a centralized source of truth that makes Bitcoin revolutionary.

As for the size of the chain, your personal blockchain can be pruned to require less data, an improvement is underway to allow it to be pruned even further, and the price/Gb of storage is still decreasing.  This is a concern, but it is being addressed, and is unlikely to become a major issue for some time.