I should be in the other thread, but since you were two were courteous enough to answer, I'm going to respond.
1. I set goals for techs. I have been making Buddhism/Hinduism my first goal, Bronze working the second, and then I start going for the worker techs as appropriate for my land condition. After that, I go for Alphabet (I think....let's you build libraries....right?)
Writing lets you build libraries.
There isn't a single tech order that works. What I do is have a list of goals that I keep updating. The goals are based on the game I want to play and my starting situation. They might be things like:
- Secure defensive tech - bronze or animal husbandry
- Key worker techs that will help early growth
- Religious techs IF I start with mysticism and can realistically found a religion.
- Techs enabling key early wonders if they are part of my strategy as opposed to an early rush.
The priority I put on them will be different from game to game. But you know that you are doing it right when things come together. Eg your defenses are hooked up before barbarians arrive, your city is working good tiles because you researched the right worker techs, your workers are never idle, early wonders become feasible because you researched the tech early enough to win the wonder race (or you avoided the wonder - if you end up trying and failing it probably means your tech order is off) etc.
All of these compete - but often you will see a right way of doing things where doing them in the right order accelerates your growth. Most often its being ruthless about not researching things you don't need immediately and aren't part of your plan.
2. I guess I don't understand when I shouldn't trade...besides trading away Iron, Copper, Horses, etc to someone I may attack. Otherwise, I check all the civs for techs I can get and extort as much money as I can for extra resources.
If you trade too often you can reach the "We think you are too advanced" limit. You don't have to worry about this with friendly civs, Mansa or if you are both weak in power.
The other main reason for not trading is diplomatic. You are often better off trading with a handful of friends and not trading with people they don't like. Your friends will like you more and give you better deals. Trading with everyone risks annoying everyone and not having any close friends.
3. I'm ok at managing a war. Unfortunately, I havn't gotten to the point where my army was capable of attacking one of theirs.
I would suggest winning some wars on Prince before going to Monarch. Depending on your starting situation you might be forced to conduct an offensive war to expand and catch up.
4. I expand to three cities rather quickly (I think that is what many people do...) but I start to have financial problems, slow down to build stuff other than settlers, and end up boxed in with only 3 cities. One problem may be that I blow all my early units fighting Barbs, lest they kill my workers and pillage my improvements.
You may not be expanding as quick as you think you are. Using slavery and chopping you can get three cities our quite quickly - often before the barbarians are a big problem. Your second city should ideally secure you a military resource (horses or copper) and you will need some troops. Axes and chariots both have good win percentages against barbarian archers and two per city should give you good defense. You can also reduce barbarians significantly by removing the fog of war.
Three cities shouldn't cause any significant financial problem. You will need to drop the slider but thats OK.
5. I've been trying to plan cities and my last game I had one really really financial city and one huge production city. I went with the strategy of chop rushing/whipping for wonders that had financial/science effects as well as a good great person rate. Another city probably could have been great but the barbarians kept trashing my improvements. The fourth city was supposed to be a Solid production city but there simply wasn't enough food to keep production high. It was actually a city i had taken culturally. I still ended up waaaaaay behind in techs and army units.
You really want more cities than that. At least six good cities so you can build things like Oxford. Which is why an early war is often necessary on Monarch.
Barbarians shouldn't be a problem once you get into the AD years - all the land will be settled by someone (or at least within visibility of a city), except for ice or desert regions that you can leave a warrior or scout on to stop barbarians from spawning. On Monarch the AI's help a lot - some games you have no barbarian threats at all because the AI's have so many units and cities that barbarians can't spawn.
Is going for religion a mistake at the Monarch level? Should I research cheaper techs instead and have religion spread to me? What should my first Queue look like? I have been doing Warrior-Warrior-Settler-Warrior/Monument/Archer/Granary-Worker or something like that. second city is Warrior/Archer/Monument-Warrior/Archer/Monument/Granary-Worker/Settler
Going for Hinduism / Buddism is a mistake if
a) You don't have mysticism
b) Its not part of your plan (if your plan is an early rush with Ghengis Khan then its not a priority).
You will need to secure some happiness though. If you don't go for a religion (you can use Oracle to get Theology or Code of laws for a later religion too) then you need some other source of happy. Good starting resources, Charismatic or prioritizing Monarchy are all options.
A good build order that I like is:
Worker/Warrior/Settler/Warrior/Settler with the second city building worker first and then troops. Your build order leaves workers very late. Which means your cities are working poor tiles. I probably get my third city established around the same time your second city is established.
What is up with Imperialism? The Settler rate is supposed to be higher....but it didn't seem to be. I built London in the middle of an area with about 6 three food tiles, and some 1 food/2 Hammer tiles. I let it grow to size FOUR and it still was 25 turns....and I had health issues.
Imperialism only gives a bonus to hammers. Not to the food that gets converted into hammers.
What is the best use of GP? I would think Prophets you build their building..but how about scientists? It seems in the long run the academy is best and I am always tempted to do that but should I be lightbulbing techs? How about Engineers? Rush stuff? Artists when on going for cultural victory? Use them as a border bomb?
There is no single best use - it all fits into your plan.
If you are behind the AIs and there are lots of good trading opportunities on the table, then lightbulbing is very effective - one GP may give you 4-5 techs.
If you are ahead or equal to the AIs then I wouldn't lightbulb. I would build shrines (if the religion is one I am committed to spreading), academy in my science center, rush a wonder that I really don't want to lose and settle otherwise.
Late game I would consider saving the GP for a golden age. If I have a big empire this can really pay off.