Yes, they are both open.
We would urge anyone visiting either location by car to make use of the car parks, and refrain from parking on the sides of the road. The car park gates are usually locked by 9pm. Please note that the through road at Shearwater is designated as a clearway, and is routinely patrolled with parking enforcement by Wiltshire Council.
Shear Water Lake is open for coarse fishing, prebooking is essential, please see https://www.longleat.co.uk/fishing for more information.