1) So you confirm, there is no delay difference between sending a small or a big amount of bitcoin?
2) It's the fees that make the difference!?
The size of the transaction in terms of the Bitcoin does not affect the speed. However, the size of the transaction fee with respect to the transaction size will matter. The miners will prefer to include those with a higher fee/byte first. This helps to ensure that they use the space in the limited 1MB block efficiently and control the spam.
3) The fees is not amount depending ?
Yup.
4) What is a correct fees actually?
It varies according to the network condition. As said, there is a limited number of transactions the miners can include in a block. The more transactions with a higher fee than you, the longer your transaction may take to confirm since they will select those transactions first. Once the block is filled, you will have to wait for the next block for a possible confirmation. Generally, a client like Bitcoin Core and Electrum has automatic fees to help you to determine the best fee according to the speed you want it to confirm. This is known as dynamic fee or floating fee.
You can also see the fees/byte to pay at bitcoinfees.21.co and input the value into your client.
5) What kind of transactions need to be online all the time?
Once you make the transaction, you can switch your computer off. When a transaction is made, the transaction is broadcasted and propagated throughout the network. Once the miners have seen it, they will consider including it in their block.
