You are misunderstanding how the system work. There is no such thing of which bitcoin. It is just a number associated with the address and there is no way to distinguish between different number.
Also, the transaction fee is used to pay for the miner who process and record the transaction in the network. Hence, the bitcoin client always ask you for the transaction fee when you want to make transaction, regardless how many address you have and how you spend bitcoin. All transaction demand the resource from the bitcoin network. Hence, not paying the fee is bad for the network because people can spam the network and affect all normal transaction.
no you are wrong
" At the moment, many transactions are typically processed in a way where no fee is expected at all, but for transactions which draw coins from many bitcoin addresses and therefore have a large data size, a small transaction fee is usually expected."https://en.bitcoin.it/wiki/Transaction_fee