Adding to the post above, you gain one population per turn as the default (meaning, you always have +1 prestige). It's possible to have negative prestige with some improvements (Fallen in Beta had a sacrifice pit for -prestige), at which point people will be leaving. But your prestige amount is exactly how much population per turn you'll be gaining.
2. What is world research?
"Goodie huts" (tiles you can explore for rewards) go up levels, and this research allows you to explore higher level goodie hut tiles.
Quests and quest tiles have a similar mechanic.
3. Heros kind of suck unless there spell casters
Not quite. Once you research armor or weapons with the Warfare tree, you can shop with them while in your territory (switch to the abilities tab with one selected, and click the shop button). The stats offer percentage increases to the equipment, so the better their equipment the higher the bonus. The main issue with them is that despite their attack/defense scaling, their HP really doesn't which makes them less good against "squads" of units (like 10 guys that attack as one).
4. How fast should one expand . and for that matter how do you use caravans
How fast is subjective. To use a caravan, train it, then tell it to go to another city. Once it reaches it, a caravan route will be created and you'll see a road joining the two cities. The caravan will move much faster on this established road, and you'll get an increase to production.
