[Ethereum] How to transfer ERC20 token to another contract and calling contracts function

The problem is that you are sending a non-zero value (1gwei in your example). If you want to transfer tokens then you have to set value to zero.

var rawTransaction = {
  "value": 0,
   ...
};

The reason is because for security functions that receive ether must have the payable modifier. Your transfer function doesn't have that modifier, and will reject any transaction with a non zero amount of ether.

function transfer(address _to, uint256 _value) public {
    _transfer(msg.sender, _to, _value);
}

You cannot send tokens directly from one address to another address. Tokens balances only exist in the Token contract storage. You necessarily have to send a transaction to the contract indicating you want to make a tranfer, so the contract can update the balances accordingly.