Does the pressure change inside a plane when it is opened for paratroopers?
When people jump off an airplane with parachutes, there are two categories:
This is normally done at lower altitudes, somewhere from 1,000 meters (3,000 ft) - 4,000 meters (13,000 ft). The airplanes used typically for this purpose do not have a pressurized cabin. So when the door opens for paratroopers to jump, pressure outside is almost the same as inside. After the jump, the door is closed and everyone is happy.
This is a Cessna 208 configured for skydiving, with a door visible on the port side of the aircraft.
These jumps are done from 4,600 meters (15000 ft) and 11,000 meters (35,000 ft). At 35,000 ft, only 26% of the Oxygen is available when compared to the amount at sea level.
When the door is opened at such high altitudes, amount of available Oxygen is no longer sufficient for humans and everyone needs to wear the Oxygen mask to avoid sickness due to high altitude. More about re-pressurization of cabins is discussed here.
As far as the paratroopers are concerned, they wear special gear, which looks like this:
When you open the door, Bernoulli's principle guarantees the pressure in the cabin will drop (yes, lower than outside).
The actual pressure difference will depend on various factors like door placement and size, aircraft slip, but mostly and especially on aircraft speed. For a normal skydiving operating speed (say <100kts) this will raise the cabin altitude by no more than 100-200 feet.