Mustang differential ratio calibration question

[S550 curacao]

Hello i have a mustang gt 2015 mt82 manual tranmission
My rear diff is 3.31 ratio but has got a humming sound
I want to buy a used differential maybe considering buying a 3.55 or 3.73 ratio

My question is
1. Can i just swap the differential without calibration of the guage cluster if i dont mind the speed being a bit off ?
Or will i have abs and traction error lights also if its not calibrated?

2. Is a automatic car differential direct plug and play for my manual gt?
Or should i find one thats was also from a manual mustang?

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[ORRadtech]

Why do you think it's the diff making noise?
These cars are pretty notorious for wheel bearing problems. I've not seen a lot about diff issues.

 

[S550 curacao]

I put the car on 4 jack stands
Left the car in first gear
And went under the car
I hear the diff making noise and feel some vibration also from the diff

 

[S550 curacao]

The rear diff bushings where torn also maybe the diff was damaged because of this

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