That hose is just a vent tube that allows air to escape as the transmission heats up and cools down.As for the vibration it is unlikely it is coming from transmission.If anything is damaged enough to vibrate it would not last two weeks must less two years.I would look closely at the fan clutch and see if you have some wobble there.The squeal could have been a belt and the air noise could have been the fan clutch locking up when it should have been free wheeling.Good luck.
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