Yes, the camera E3 menu only controls the cameras own internal flash. It does not affect a hot shoe flash, which ordinarily has its own menu (SB-300/SB-400 are the only exceptions, I think, part of the Nikon system).
If the camera flash door is shut, the camera E3 menu has no effect on anything, simply does not matter what it says then.
And yes, when the camera meters that TTL preflash, and instead sees also the Vivitar flashing, triggered by the preflash (and at much higher level than the minimum preflash), the camera thinks that was a very strong preflash, and programs the final flash much lower.
Said another way (and I am just making up numbers), but the preflash is a minimum power level, like maybe 1/128 power. The camera meters it and computes that the final flash ought to be, say.... about 5 stops stronger (say 1/4 power). So it tells the flash to increase its power level 5 stops for the final flash.
But if the Vivitar also triggers due to the preflash, maybe say at full power level. And the camera meters all this, and says (for example), wow! That preflash is a couple of stops too much already, and it tries to set a much lower the flash level. I don't know what its capability is then, but a much weaker flash could be expected.
