It is faction wide. Like most other modifiers, it applies no matter if a unit actually has the base stat or not. So in this case, even those without an essence stat or that aren't normal units (summons, guardian units) will get a boost.

2. Do your units only heal if they are garrisonned in a city?

They also heal when in your own territory at a rate of 1 per turn.

3. Does city population affect anything (i.e. production, gold), or is it just another resource for creating soldiers? (Besides levelling up the city, that is.)

It affects the aura of influence your city projects. At various thresholds, it will increase in size.

4. What is the difference between the Teleport and Teleport Friends spells? They both have the same description, but Teleport is a lot cheaper to cast.

Don't know.

5. Why do my spells have huge maximum damages (like 144 for a fireball) yet the damage from them is only ~7 average? Am I missing something? Is there some hidden magic defense level?

Like all damage in the game, it's 1 to max but it is also defended against by normal defense.

6. When you create a sovereign, you specify a Wisdom score. Is this the same as Essence? If not, how are they different, and why can't you increase wisdom?

It's the same. It's probably just poor consistency; it should really just be changed to essence.

7. What is the difference between the food and the healing potion that are available early in the game? They both say '5 hearts' on the description, which I assume means they heal 5 health, but the food is cheaper.

Haven't tried them myself; perhaps just when you can use tem.