I can't find how many Fetishes are summoned when you cast Fetish Army.
Is it random each time they're summoned?
Does it depend on the caster level?
Do they actually have limited life, or are they invincible the time they last?
It is always 5 fetishes (all runes except the following), 7 with Tiki Torchers or Head Hunters and 8 with Legion of Daggers.
As far as I know, they are invulnerable. I read in the battlenet forum (discussing an inferno-viable summoner build) that they count as minions, though. So you would benefit from crowd control, melee reflect or life steal / life on hit effects. This also apllies to Fetish Sycophants.
According to my little experience using this spell, the base number of fetishes is always 5 and the different runes can make this number vary.
I used them when I had a lower level and by then the enemies didn't kill any of them. They flash, however, when they receive an attack, so it could very well be that their life points are limited.