Does my vented septic tank even require traps and vents near the actual fixture connections?
Take a straw.  Suck up some liquid, and put your finger over the top.  Notice how the liquid doesn't fall out the bottom of the straw.  That's a vacuum lock, and it is one of the reasons why you need to vent your drains.  Poorly vented drains don't drain well, and you'll get clicking and bubbling.  Your toilet may fail to clear the payload.    So regardless of any venting in the septic tank, you need to have appropriate drain venting.