The trapped dry air pushes outward on the tube, and the atmospheric pressure pushes inward on the tube, hence it will be atmospheric minus the exerted pressure.
For the second, the weight of the thread is no longer compressing the trapped air, and instead when the mercury slips downward, a vacuum will form, and this will keep the mercury upward. Atmospheric pressure acts on the tube and pushes on the mercury, while the dry air pulls inward on the tube and mercury.
Hence that's my reasoning. Hope I helped!