#1 - It should be an easy tow. With the Trailblazer, it will hardly even be noticeable except when braking. Just remember to give yourself LOTS more room to stop.
#2 - This question is best answered by asking where you are going to tow. Laws vary from state to state and province to province. There are specific limits in every jurisdiction you are going to be traveling through. Some can be as light as 1000 pounds and some as high as 4000 pounds, so you see how much it varies.
#3 - You should be fine without them. The Trailblazer can easily handle the 300 to 350 pounds of tongue weight you will need to prevent swaying. GM requires weight distribution hitches and sway bars above 4000 pounds.
The specification you need to watch is the GCWR or Gross Combined Weight Rating. This is the weight of the vehicle, passengers, cargo, fuel, trailer and trailer cargo. It varies a bit but runs around 10,000 pounds. (Check your door label for your actual GCWR.) It is easy to forget that a 3000 pound trailer can edge upward pretty quickly to 4000 pounds when you add fuel in the ATV tanks, plus optional gear, plus all the extra stuff you are carrying in the trailer. Now add in 4 husky guys with a weekend supply of beer, a full tank of gas, half a pack of smokes and 4 pairs of sunglasses, and you are now edging the upper limits of your GCWR.
Experienced tow-ers always see the GCWR as the most important towing spec. One may think manufacturers want to have conservative ratings but they also want high numbers that look good in comparison to other makes in the same class, so they end up pretty accurate.