How much illumination do the background stars provide?
Although sources go way back, the current best estimate seems to be that of Abdul Ahad from March 2004:


  For an observer located anywhere within the Solar System - excluding the contribution of light from 
  the Sun (Solar constant) - provisional integrations using stellar magnitude data sourced from astronomical catalogs places an an approximation for this constant in the range:  -6.0 &lt;= mAhad &lt;= -7.0
  having a mid-point value of -6.5 magnitudes as a consensus within the astronomical community. This 
  is the total integrated brightness of the night sky that we visually experience from Earth. 


Other sources for same value:


  -6.5. Brighter than Venus, but dimmer than the brightest Iridium satellite flares.