I want to add a single outlet at this box, which I'm assuming is just a junction box(?). What parts would I need to buy in order to install an outlet here?

 

First verify that you have a 120 volt branch circuit breakered at no more than 20 amps and not serving certain dedicated purposes such as a laundry area or bathroom or kitchen counter, or a high wattage fan/heater or comparable device, coming into the box.
Find a metal box cover with cutout for a duplex receptacle and that fits this box.. The receptacle unit will be fastened to the cover, not to the box.

 

I think I found the part you're talking about...
https://www.homedepot.com/p/Steel-Ci...-25R/202592860
Now how would I cover up the unused half of the opening? Again I'm only wanting to add one outlet.
This circuit is already potentially overloaded. I've added up all of the wattage, included in the circuit. I have a warning sign telling guests not to run the hairdryer at the same time as the ceiling heater.
The office refrigerator has already been running on this circuit. I'm simply wanting to have the refrigerator plug connected inside this closet instead of outside. It's unsightly to continue to run the cord out the closet to the existing outlet.

 

You've linked to the wrong cover.Try this one..... 1900 receptacle plate.

 

One more question. Is there an attachment that can extend the depth of the box outward?

 

I have seen attachments that extend the depth of the box outward but I don't specifically recall one for your box size.

The cover that PJmax suggests has a small bulge out, I think 1/4 inch..

 

Yes they make extension rings.

https://www.graybar.com/store/en/gb/...xtension-rings

 

You could also use a deep mud ring. They range from 1/2" to well over an inch.
Mud ring

 

I found a part at HomeDepot that indeed extends about the length of an outlet. Thanks.

 

Andy have you confirmed yet that this circuit you want to tap into in the jbox is in fact a 120V circuit? I see what looks like an appliance cord next to it. What is this cord for and is it plugged into the same circuit as this jbox is connected to.

 

Small office refrigerator in the closet. Actually this circuit does not run to the bathroom as I previously said.