New silly question...
What is this, and can I drive with it like that? Just noticed it this morning. Don't exactly want to call someone and be like "the thing isn't attached to the other thing, that cool?", so here we are... Can I just stick it back in there and call it a day?

 

That's the fresh air end of your air filter housing. I can't imagine it would cause any problems to drive like that - it will pull in underhood air (warmer) and maybe be a touch louder.

You should able to just shove it back together.

 

If you want to save your engine you should get rid of that k&n filter that sticker says is in there

At best they don't work well, at worst if oiled they coat your MAF with oil and then it doesn't work well. Seriously, they pass a lot more dirt into your engine than the stock filter.

Looks like somebody tried to do some kind of gotts mod and duct tape it together....... The idea is that the stock air inlet is too small diameter and is restrictive.... So you adapt your own slightly larger one. You will read all kind of people say "oh it feels like I got a few more horsepower.".... I don't ever recall seeing hard evidence such as Dyno output at the RPM you drive it on the street....625-2500 rpm. Thars usually a reason for that.......

 

Looks like the filter housing clamp, the big circular one, is not fully seated. Better check it. You might have a gap somewhere letting dust and dirt past your oily K&N filter.