The wallets set a fee based on those numbers, but that is not what you have to pay. The fee is completely controlled by the wallet user and can be set as high or low as you like. If you are using a wallet or online wallet that does not display the option for you, then the wallet is choosing and it is choosing based on the numbers that people are indicating here, but it is still the software that is choosing and only because you were dumb enough to let it control your life and finanaces.
But you find the on pop up says that fees is only for miner not for wallet provider. For your view what would be the options to identify it whether it is goes for miners or wallet providers alone. In my transaction I checked the default transaction fee in blockchain wallet. It states that fees is around 0.00075 btc for a transaction. Still I am confused why again they reduced the fees little now.
Fees go to the miners. The wallet software just gives suggestions as to what the fee should be, or picks what it believes the fee should be.
The fee is based on the supply of space in a block (1mb) and demand for that space (with some stickiness of course). So the reason fees fluctuate is because the number of transactions seeking to be included in a block fluctuates. Recently there have been a lot of transactions (probably spam transactions since they suddenly dropped off) that were filling up blocks and causing fees to rise.