Quick questions? Really?
When a City State asks anyone to do a quest, and you complete it, does that make the City State, wherever they are located, regardless if they are road/route hooked up to you or not:
a. Start sharing their entire resources with you?
b. Start giving you a certain amount of gold, per turn, or all at once, too?
Satisfying a quest will earn influence (amount varies with the quest), just like gifts of gold. Amount of influence determines whether you are friends (30 influence) or allied (greater of 60 influence or, if more than one civ is above 60, more influence than any other civ). Each turn you lose influence, so you need to keep satisfying quests, giving gifts of gold, etc.
Each type of CS gives different benefits at friend and ally level. At friend level, maritimes give food to your capital, culturals give culture (amount rises by era), religious give faith (amount also rises with era), militaristic will give land units, and mercantiles give happiness. When you achieve ally status, you get the CS's luxuries and strategic resources, but any duplicate luxuries are just that--duplicates --no extra happiness, but you can trade away your own copies for gold or another luxury. In addition, all but mercantiles give more of what they gave at friend level (militaristics give units more frequently and maritimes give 1 food to each city).
Now some more related questions:
c. What happens if you already have the particular resource that they have, do you still get the +1 happiness (or whatever a resource brings) for that resource, too?
Answered above - no.
d. What is the difference between having them at war, neutral, friends, or allies? Do they increasingly share more resources, sliding up the "likeness" scale, from war with you to allies?
Magic levels are friend and ally. War is a not-helpful place to be.
e. We have never seen any allied City States actually go to war with someone we are already at war with, even though it is announced that they do; even the aggressive City States show no military support. Are we missing something? It seems that being an Ally is a waste.
CSs will not send units more than a short distance from their culture borders. They will not send units across the map to help you. But an allied CS that is next to an enemy city will attack the city and can conquer cities.
f. Puppet, Annex, or Raze: Isn't it always better to Annex the City State, as you can lighten the Annexed City State's unhappiness by immediately building a Courthouse, THEN, have the City State beeline through the "happiness buildings", if that is what a player wanted?
First, you need a really good reason to conquer a city state -- the friend and ally bonuses go away on conquering and often cannot be replicated by the conquered city on its own. But, if you want to kill CSs, like any conquered city, start off puppeting them -- while they're in revolt you can't do anything with them. Annex decision is same for CSs as for regular cities. If you don't mind the policy cost increase, go ahead and annex, but shouldn't do so until you have the gold to rush-buy a courthouse.
g. Whenever I take over a City State I rarely see a bump in my overall score (as compared to taking over a Civ's town); is that only because City States aren't really worth fighting with/taking over vs just doing quests for them and garnering their resources?
Basically.
h. Trading with City State to increase your happiness: Does it make sense to trade with City States to bump your happiness when they have an extra resource that you could use, and, as barter, you trade with them one of your extra resources, or use money in lieu of this? It would seem to me that you would increase your happiness +1 per turn (or whatever a "happiness per resource" brings). Redundant resources that they give you mean nothing for your happiness, I think...
Can't trade with CSs. All you can do is give gifts of gold and fulfill quests.
