I don't understand the plate or the ball demonstrations. Was air being sucked or blown in those cases?

Air was being blown in both cases. In the plate demonstration, air from a hose was blown between two closely spaced plates. The air had to move very quickly to get through the narrow space between the plates, so its kinetic energy was very high. To offset its rise in speed, the air's pressure had to drop. It dropped so low that it became less than atmospheric pressure. The surrounding air then squeezed the two plates together so that they didn't fall apart. In the ball and funnel demonstration, air blow out of the funnel had to speed up as it flowed through the narrow space between the funnel and the ball. As it did, its pressure dropped. The slow-moving air under the ball then held the ball against the funnel, even though it was upside-down.

How does the aspirator pump work?

The water aspirator pump is essentially a pipe with a narrowing in it. As water flows through that narrowing, it speeds up and its pressure drops. It's exchanging its pressure energy for kinetic energy. A tiny opening in the side of the narrowing allows water or air to enter the high speed flow. Since the pressure in that high speed flow is very low, atmospheric pressure pushes fluids through that tiny opening and into the flow. The flow pumps fluids through the opening and into the water stream. If you connect a hose to the tiny opening, you can suck chemicals up the hose and into the water stream.

How does the fan boost the pressure back up so the air will go back into the room?

The fan is a rotating assembly of ramps. As the ramps move, they sweep the air from one side of the fan to the other and do work on that air. The air either accelerates as the fan blades spin past, or its pressure builds up. Either way, its total energy increases. The fan can take low pressure air from one side and whisk it over to the other side where the pressure is higher. It can push air against the natural direction of flow (from high pressure to low pressure). It's essentially a pump for air.

What do open pours in the vacuum bag have to do with anything?

The vacuum bag has pores in its surface. If the bag were air tight, then it would quickly stop the air flow. But it has tiny holes (the pores) through which air can flow but dust can't. These pores block the dust and prevent it from returning to the room air. The dust accumulates in the vacuum bag and the air doesn't.

Why does dust settle on the moving blades of a fan?

As the air flows across the blades of a fan, the dust particles in it occasionally pierce through the airflow and hit the blades. The same sort of process occurs when a bug hits the windshield of a car; the bug would normally follow the airflow but its inertia prevents it from moving out of the way quickly enough and it hit. Once a dust particle hits the fan blades, there isn't much to remove it. The air moves remarkably slowly right at the surface of the fan because that surface layer of air experiences lots of viscous drag. Even though the air is moving swiftly only a few millimeters away, the air right on the fan blade is almost stationary. Thus the dust can cling to the blade indefinitely.