What is making my 2004 Ford Expedition accelerate sluggishly?

Your poor performance can be due to a loss of air flow either in the intake or even in the exhaust. Sometimes catalytic converters rust out on the inside and collapse in on themseves causing a blockage. You can whack on the converter with your hand or a rubber mallet and see if it sounds like loose material is in it. I am giving you a walk through diaganostic for your situation. When it talks about pulling codes and doing test like for fuel pressure. Advance Auto and Auto Zone both will pull codes for free and both loan out specialty tools such as would be needed for a fuel pressure test which I reccomend. Just use the link below;

https://www.2carpros.com/articles/engine-has-low-power-output

As far as your transmission, you may have done some damamage but you would notice a change in its performance if it were bad. It is not good to pop them into gear or to put them into a forward gear whwile rolling backwards. But, thjey can take a little abuse before failing.

My brakes are also performing poorly. I got the pads changed in March. I just looked at the fluid, and it is a very dark, very murky green. When I push on the brake pedal, it is much firmer than it was a few weeks ago, and it takes twice the distance to stop.

On most Fords the power steering pump provides the power assist to the brakes. You can tell by looking at the brake master cylinder and if you have a pie shaped metal part that has a vacuum line running to the manifold it is vacuum assisted. If it is a smaller metal part with lines running towards the power steering pump, it is power steering pressure assisted. So, You could have an issue with debris clogging the brake lines and you might want to flush them until clean fluid comes out the bleed screws. Then you might have a failing power steering pump which is making the brakes perform poorly.

Would that also affect the power steering?

I my experience you feel it in the brakes before it affects the power steering. I have a Mustang and it fealt like the brakes were hard to press to come to a stop. It started making a squealing noise when started that would go away. The steering fealt fine but the pump was bad. I was able to grab the power steering pump pulley and move it around and feel that it had play in it.

I'll look into that. Also, the rear A/C unit is making a clicking noise. I think it's the actuators. Is that correct?

Does it click when you change something on the A/C controls or does it contantly click or intermitantly?

It clicks constantly, but gets very loud when you turn the blower on.

That sounds like actuator or there may be an issue with the vent door.

How can I tell if it's the vent door?

When you turn the vents from heat to A/C, check and see if airflow changes. Do not change fan speed.