Question about air pockets?

Yes they do, and the air throughout the air pocket will be at the same pressure* as the water directly below the air-water interface, since air is compressible, but water is not

Imagine an air-filled cave with an underwater entrance and no opening at the top. As the water level rises outside the cave (e.g. with a rising tide), more water will flow into the cave. The water level within the cave will therefore rise, but since the air cannot escape, this rise will be 'cushioned' by the increasing air pressure above it.

When the water level reaches its maximum, the airpocket will be compressed to a pressure equal to the water pressure below it, which will be related to the vertical distance between the 'external' water level and the 'cave' water level, e.g. if the 'air-pocket' water level is 15 m (= 1.5 ata) below 'sea level' (1 ata), the air-pocket pressure will be 1 + 1.5 = 2.5 ata.

*Although in theory the pressure at the top of the pocket might be lower than that at the bottom, the difference will be non-measureable -- it takes an 'air-column' approximately 100 km (100 000 m) tall to deliver the same pressure per square meter (i.e. ~1 ata at sea level) as a 10 m water-column, and more than half of that 100 000 m 'air-weight' is concentrated into the lowest 5000-10 000 m.

My rental kitchen cabinets are very old, so I decided to protect and cover them up with wood pattern contact paper. I first cleaned the surface and then cut the contact paper to size. I peeled back the contact paper about 2 inches in width and taped from the top right and left corners. Once I had taped everything in the right place, then I peeled away the backing as my hand swept left and right until the whole area was covered. The problem is, there are still lots of bubbles everywhere. I used a car windshield scraper, but it did not help. Is there better way to do this? Please advise.

yes but no and yes but no