The conditions being:
You don't need more than one
city, for starters. (For reasons that are mathematical and a bit complicated to sum up.). Also, everything that makes it possible to access 
resources around that city. (Well, Agriculture, for starters, and Pottery of course.) This because, you might wanna turn some of the citizens into specialists in that city to create further points. (The other ones feed the specialists, you get?) The easiest path would be to get Code of Laws and adopt Caste System (unlimited specialists). This should get you started.
stands for Science. You accumulate every turn in your cities, and once you've amassed enough you get the Tech you're currently researching. Then the process starts all over again. But its important to know that the percentage isn't what counts, but rather how many you produce per turn and city. You can see this in the Domestic Advisor (F1), listed per city. There are other ways to produce than to just convert your 
(Commerce) into research (via the % setting). Scientist specialists come to mind (see above)...
In addition to what IAM said, you can also found one of two corporations: Sid's Sushi or Cereal Mills. Each of them transform excess food resources into additional food in any city where the corp is spread.
Citizens from your city can only be assigned to work the 20 tiles in the city's "fat cross"--the number of tiles contained within the city's first border expansion. As the city's culture grows, its borders will continue to expand to include more tiles outside the fat cross. You can improve these tiles, and it is usually to your advantage to do so. However, your citizens will never be able to directly work those tiles unless you build another city nearby.
You need to get the Rhye's and Fall of Civilization mod. Its a historical mod that spawns all Civs on their historical dates, so when a new Civ is born the player is prompted to take control of it (if he so wishes). You can only do this once, though, but if you say start off as Rome in the Classical Age you could switch to the Turks in the Renaissance Age. (America, of course, spawns last, and only a handful Civs spawn in the Stone Age.)
You've got the second point correct, sir.
(Commerce) in your cities. is mainly generated from 1. the tiles you work from within your city screen, and 2. the trade routes (normally 1-4 or so) listed at the top portion of your left pane inside the city screen. It lists the cities your city is trading with (internal or international) and gives you an amount of per turn and trade route. from worked tiles and an additional 5 from a few trade routes, as an example. This adds up to 10 in total, which is then converted into production of 
, , 
and 
in the proportions (counted in percentage) you assign on the top left corner of your screen. (Above the trade routes and their yields when inside the city screen.) or to the total output of in the city. It's only a multiplier for the trade routes listed. The main thing is that its useful if you got many and/or good trade routes in that city. Otherwise not so.
EDIT: Whoops, cross posted with Baldyr.
You are correct on all points.
You need to get the Rhye's and Fall of Civilization mod. Its a historical mod that spawns all Civs on their historical dates, so when a new Civ is born the player is prompted to take control of it (if he so wishes). You can only do this once, though, but if you say start off as Rome in the Classical Age you could switch to the Turks in the Renaissance Age. (America, of course, spawns last, and only a handful Civs spawn in the Stone Age.)
There is also a version of RFC called RFC RAND which uses random maps (instead of the Earth map of the original mod), and runs much like a regular Civ Game, only far better, in my humble opinion.
You will find what you need here.
