If I wanted to use them correctly, how would I?
I'm still confused about the details but this part I can answer.
These types of wall plates are used to hide the wiring for wall mounted TVs. You have an outlet behind the TV so that you don't have a power plug running down the wall and you have an opening that allows access to the stud cavity behind so you can run low voltage wires (HDMI, coaxial for cable or antenna, network, digital audio, speakers, etc) behind the wall down to the corresponding outlet in the lower mounted faceplate.
Next to the opening on the lower faceplace can be a number of different fixtures. Either an electrical outlet or video, data or voice jacks.
The outlet would be for things like DVR players that may be on a shelf or small cabinet.
The cable pass through holes are not intended to be used for mains power and as Tester has indicated it is not wise to use it for that.
I can't tell from your picture if the bottom receptacle is a combination coax/network or a male 110 receptacle.
If it's a male 110 receptacle that doesn't make any sense why it would be connected via extension cord to the other outlet. The only thing I can think of is that the both outlets are supposed to be on the same circuit but somehow the connection between the two was broken which may have resulted in other fixtures further down the circuit not operating. That's just a guess but the only reason I can think of why it would be like that.
There's no reason to have a male 110 near entertainment equipment. My advice would be to get an electrician to sort things out because when people do strange things like that it's frequently a temporary fix for a more serious problem.