Say I'm way out in deep space and on EVA. If I turn off all sources of illumination, can I basically still see, or am I severely impaired by darkness? Of course I can still see the stars, but will they illuminate myself and my ship enough? I suppose if it's really bad I could still at least locate my ship by looking for a ship-shaped gap in the stars. What kind of light level are we approximately expecting, in the context of human visual impairment and ability to move and do work?
That depends on the color of the ship
According to this book (Sensation and Perception, AvHugh Foley, Margaret Matlin):
Riggs (1971) notes that in starlight (luminance of about 0.0003 cd/m2), we can see the white pages of a book but not the writing on them. In moonlight (luminance of about 0.03 cd/m2), we can notice separate letters but not read the text. (In other words, if you have a romantic notion of reading poetry by moonlight, take a flashlight!).
Starlight in deep space will be slightly better, roughly 30%. But that is not nearly enough to make a significant difference. So let us say that starlight provides ~4*10-4 cd/m2.
Humans have night vision (Scotopic vision) between 10-3 to 10-6 cd/m2. And since starlight is ~4*10-4 cd/m2 in deep space, that should be enough to see a perfectly white object.
So if your starship is bright white, you should be able to discern it even in starlight. If it is not bright white however, you might be in trouble, or you may have to employ your suggestion of looking for the perfectly black spot in the background.
As far as doing any kind of practical work however, no. You will not be able to make out any kind of details. You will be essentially colour blind. You will be able to see the presence of "large" white/light objects, but details will be impossible to make out.
These notes more or less answer your question. Look for example at figure 10 on page 8. Starlight in space will be somewhat brighter than on Earth, partly because it is coming from all around and partly because the atmosphere isn't dimming it, but I doubt that makes as much as a factor of 10 difference. So you would still be able to see things (once you had fully adapted to the darkness) but with no colour vision and poor resolution.
I have two thoughts on this:
1.) You could do the following:
Go out into the desert, in a moonless night, far away from civilization and artificial light sources. Choose a desert at high latitudes (remember Icy regions can also count as deserts).
Around midnight, that is the illumination level that you can expect. If you can work in that, then you will be able to work in deep space.
2.) One could as well do a little thought experiment: When reaching very dark levels of brightness, experience from astronomy tells us, that the human limit in dark vision for stellar magnitudes is around $m=-6$ (see also Uwe's comment about astronomical magnitudes, the scale is essentially upside down and a change of $m$ of 5 is a factor of 100 in luminosity).
The adaptation page on wiki also mentioned that the contrast the human eye can perceive at any given time can span a factor of ~1000. And you need contrast to be able to discern things! i.e. to work with them.
From here on the situation depends on what you want to do:
- Being attached to your ship, working outside, and assuming the ship has a reflecting Albedo of ~1, your ship will be as bright as the other side of the sky. So if there are at least 1000 magnitude $-6$ stars behind you, that should give you enough contrast as well as enough brightness to work.
I'm not 100% sure about this statement, it seems so simple, but that was the result of my thinking.
- Inside your ship, without power and illumination it might become problematic. You'd need to make sure that the interesting surface you want to work on is being shone upon by the 1000 $m=-6$ stars through your spacecraft windows. Depending on the region of the galaxy where you're in, that might prove difficult.
- If you're far away from the craft and trying to find it, it's reflection surface brightness will decrease of course with $1/r^2$. So depending how bright the background is against which you're trying to find it, you might quickly end up 'looking for shadows'.