It's not a junction box. It looks like what is called a shallow pan box, and those boxes typically do not have sufficient volume to allow you to legally add more wires. Unless you are permanently disconnecting whatever is attached to the power in that box, you're going to have to add more volume by using a box extender or switching that box out for a larger one. I'm totally supportive of DIY, except in regard to electrical work where someone has little knowledge of how to do things safely. I don't mean to be insulting, but please get a basic book on how to do safe wiring or get the help of a knowledgeable friend before you redo this. You need to understand safe work practices, proper grounding, and box fill limits. When I started doing my own electrical years ago, I thought I knew enough, and then subsequently realized that I had made a couple of beginner's mistakes that could have posed a shock hazard and violated code. You don't know what you don't know at first.

The writing on that cover reads 'for micro wave heating only' and it is marked as dishwasher safe, so it looks very much like an improvised cover for the box. If you are going to be doing work it is probably worth replacing it with a properly covered box, or, as suggested above, a larger box that will accommodate the additional wiring you need.
I am another who learned his electrical abilities by having to correct some potentially dangerous mistakes I'd made. Most DIY electrical wiring is quite easy, but even easier to get wrong if you don't do a bit of learning.

Looking at that photo again, I think Nick is right. It's not even a pan box...somebody salvaged a part of a microwave to make a "box" which would not comply with code in the first place in that application, even if it had a cover. Get rid of that and put a properly-sized, code-compliant box in its place. It will cost you a buck or two that the former owner wasn't prepared to spend, I guess. If that is representative of the kind of electrical work the former owner did, it might be a good idea to pay an electrician for an hour or two of his time to see what other "innovative" shortcuts were done throughout the house that are possibly illegal and dangerous.

electrician it is! I'm happy to admit I know nothing about wiring!

You also need a light to be controlled by a light switch. Some random junction box (even if it was properly installed) may not be controlled by a switch.

That box is outside? I'd love to see a photo from further back that shows the area. What's the material surrounding the box? Is it siding? Is the microwave plastic plate held to the wall with just that little nail or is it glued too? Definitely creative! :) But obviously not the proper way to do it.