Which institutes or companies built the cameras on the following
Soviet/Russian spacecraft: Luna 9 (moon lander - 1966), Mars 3 (Mars
lander - 1971), Venera 13&14 (Venus landers - 1981)?

http://medfmt.8k.com/mf/pentacon6.html

Here is their medium format camera until they changed to a german
camera. I would guess that the later cameras are not Russian either.
But if you don't get an answer, try sending your question to these
people listed here.

FYI: Kiev, and Krasnogorsk are two large camera manufacturers that you
might search and research. There are many more, but these are the ones
I have heard about for years, and owned.

Kiev I think is best known for its Leica rip offs. Krasnogorsk makes
motion picture cameras.

I think much of the Russian optics industry is based on German
imported designers, designs following WWII.

You might also contact this company that specializes in Russian
cameras, they probably know the history backward and forward for the
Russian Optics industry.  http://www.kievcamera.com/