Hi,
The noise is likely because the fan clutch is fully locked and turning the fan blade as fast as it can. Does it do this when the vehicle is cold and first started?
As far as the MPG and rough idle, the fan does place a bit of a load on the engine, but I don't think it would be too noticeable in the MPG. However, anything is possible. Also, the sound itself can cause you to feel there is a rough idle simply because of the added load and sound itself.
Take a look through this link. It explains the most common symptoms related to a bad fan clutch.
https://www.2carpros.com/articles/fan-clutch-symptoms
Here is a link that shows in general how one is replaced:
https://www.2carpros.com/articles/fan-clutch-removal
As far as oil consumption, that is a tough one. There really isn't anything related to the fan clutch that would cause it. How much oil is being used? For example, every 1,000 miles you need to add a quart.
I attached the directions below for fan clutch replacement. See if there is anything you missed. If you didn't miss anything and the clutch is fully engaged at all times, you may have gotten a bad clutch.
Let me know.
Take care,
Joe
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Saturday, May 29th, 2021 AT 9:16 PM