No, the fees are "flat" (they are not completely flat, but they are higher with amounts of inputs) = they do not depend on the amount. They depend on the amount of space in Bytes the transaction demands from blockchain.
There is no min and max. Min is always 0, but most probably it will not go through, because the network capacity is ~ 3tx/sec and there is kind of bidding and the 0 fee is now almost always outbid by the others.
There is also no max. It is up to you how much you wanna pay. This thread is about it.
There is no central authority in bitcoin, therefore there is nobody except pure market, who can set min or max fee. There are only the processors = the miners, who can discard transactions under certain fee. But if one decides for that, the other may still accept it.
You understand it wrong.
If you talk to God, you are praying; If God talks to you, you have schizophrenia.