Is it normal for this black drainage tube to just end mid-air?

That copper tube with the red cap is definitely a service stub. When these units are manufactured, that's the port they use to vacuum out the air and pump in the refrigerant charge. Once the levels are right, they crimp the copper shut and put that plastic cap on just to protect the sharp edge. You shouldn't ever need to mess with it unless you are a tech with a piercing valve trying to recharge a leak. It is completly sealed, so you don't have to worry about it leaking gas tonight. As for the black tube, it is almost certainly an internal drain for the upper evaporator coil. In alot of these portable or window units, the water collects in a top tray first and then drains down to the main base pan. The reason it doesn't go all the way to the floor of the unit is usually to prevent siphoning or backflow. If the bottom pan gets too full, you do not want that dirty water getting sucked back up or causing a blockage in the line. It is also posible that tube is positioned to drip water directly onto the fan's **slinger ring**. Most modern units are designed to splash that condensate water onto the hot condenser coils to help evaporate it and improve efficiency. If it looks like it is just hanging in space, it is likely aimed at a specific spot on the base pan or near the fan shroud where that water can be utilized. Double-check the black tube to make sure it isn't an electrical wire. If it has any printing on the side like "600V," it's just a power lead to the fan motor or a sensor. But if it is hollow, it is a drain. You likely didn't knock anything loose; that's just how the internal plumbing looks on these mass-produced units. Go ahead and fire it up. Just make sure the outer housing is back on tight so the airflow moves correctly, or it won't cool effectively anyway.

That makes so much sense about the slinger ring. I always wondered why my unit makes that weird splashing or pitter-patter sound when it gets really humid out. I thougth maybe rain got inside or something was loose, but it's acutally a feature?

If that water is just dripping into the bottom pan to be splashed around, does it ever get gross in there? I'm worried about mold or gunk building up since I'm already cleaning it. Should I drop one of those AC treatment tablets in the pan before I close it up, or is that overkill for a unit like this?

Yeah, the gunk is real. If you don't stay on top of it, that base pan can turn into a swamp. I ussually toss a couple of those condensate pan tablets in there once a month during the peak of summer. They keep the slime from clogging up the drain or smelling like a wet basement.

Also, check that the unit has a slight tilt toward the back. If it’s perfectly level or tilted forward, that water sits in the front corners where the fan can’t reach it, and that’s when you get the nasty smells. Just a quarter-inch lean is all you need to keep things moving.

If that tube looks a bit fuzzy, I ussually just snake a long zip tie or a pipe cleaner through it to make sure it's clear. Dust turns into mud fast once it gets wet. Another tip: check the rubber drain plug on the back. Some people pull it out to stop the splashing sound, but you'll lose some cooling efficiency if the water isn't hitting the coils. I keep mine plugged, but I pull it once a year just to flush out the heavy sediment that the tablets don't always catch.