Biking for Idiots

1. Not sure - someone else who knows more about bikes might be able to answer, but my guess is that there is no "exact" answer for this, other than yes, slicks will help some, and paved roads are faster than dirt trails.

2. Yes, cages are better than platforms without cages, since you can utilize a fuller pedal stroke, than just mashing down with your quads. You'll get a little more power.

3. If you have toe cages, you should just wear sneakers. The special cycling shoes are only necessary if you are using a clipless system. Just wear your sneakers and you'll have a super-fast T2

I don't know the answer to #1, but try it.  Take your bike on the road.  Put the slicks on if you already own them.  Train like you plan to race.

Cages will help you apply power more evenly around the pedal stroke.  You'll need to train in them to get the benefit, otherwise they just make mounting the bike harder and more likely to crash at the mount line.

If using flats or toe clips (cages) just use your running shoes.  You'll save time in transition.  

And in the interest of the thread currently going on and on, I'm going to say that I was going on the notion of simplicity. For your first race, or first few races, it's not NECESSARY. Esp. since it's 13 miles on a mountain bike with toe cages. How much time and power is wearing mtb/cycling shoes REALLY going to save or gain? Let's be honest. For the vast majority of newb triathletes who maybe don't have all the gear and don't want to spend a lot, sneakers are absolutely fine.