Could diverticulosis make me pass out during normal, everyday activities?

Shouldn't. This doesn't sound like something diverticulosis would cause. I would get evaluated for another cause for your passing out.
No. Diverticulosis is quite common. It is estimated that half of americans have diverticulosis by age 50 as we don't eat as much fiber as we are built to eat. It won't make you pass out. When there is associated inflammation, it is termed diverticulitis: the -itis meaning inflammation. This usually causes significant pain, often in the left lower abdomen, sometimes fever.
No. Diverticulosis is a condition where small pockets form along the wall of the colon. If one of these pockets rupture, inflammation occurs causing diverticulitis. Rarely, a small blood vessel within the diverticulum can open up, causing intestinal bleeding. Your fainting spells are worrisome; you should see a primary care physician asap.