The differential fluid appears to be coming out of the vent hose?

Yep, this can happen when the differential overheats due to gear oil that needs to be replaced or there is a mechanical failure causing the problem, either way I would remove the rear diff cover to inspect the gears and fluid conditioner, (check the fluid for metal flakes). Here is a generic guide to help you step by step with instructions in the diagrams below to show you how on your car:

https://www.2carpros.com/articles/differential-service

Check out the images (below). Please upload pictures or videos in your response to any problems so we can see what to help you with.

Okay, there is also a hum or something is vibrating when I let off the accelerator above 60+. Could it be the gears or the driveshaft?

Yep, is the hum coming from the rear of the car? If so, it could be the rear end is having an issue. I would remove the rear cover to see what's going on. Also, you can remove the driveshaft to check the U joints.

Here is a generic guide to help you step by step with instructions in the diagrams below to show you how on your car.

https://www.2carpros.com/articles/how-to-remove-a-drive-shaft

This guide can help as well:

https://www.2carpros.com/articles/how-u-joints-work

Check out the images (below). Please let us know what happens.

Yes it is.

Yep, this can be an issue, please upload images or a shot video of the problem once you have done the work.