I see. Why a 2-move unit specifically? To be honest, I am completely clueless about using this GG unit. Any other important aspect/function of GG I should know?
Because a 2

(or 3

, with Morale) GG medic can move around much easier, and get to where units are that need healing faster. It's especially necessary when you've got an army comprised of 2

units, since a Great Medic that can't keep up with them will slow your war machine down.
I'm really sorry, but I don't quite follow. Can you explain?
As I mentioned before, the general strategy in civ IV is to beeline Liberalism, lib a key military tech as the first person to research Liberalism gets a free technology, and roll over the world with said key military tech before the AIs are able to grab something quickly enough to stop your momentum from putting you in a winning position. The way that most people tend to beeline lib, as Lib itself and especially it's prerequisite tech, Education, is very expensive, is to use a Great Scientist to bulb them - that is, use a Great Person to "lightbulb" a technology, basically consume the great person to immediately dump hundreds upon hundreds of beakers into a tech. The way to generate a lot of great people is to run the Pacifism civic, which gives you +100%

(great person points, GPP) in all cities that has your state religion present, and to use another great person to start a Golden Age (+100%

in all cities, can swap civics without incurring Anarchy, among other things). Use this combination to generate two or three Great Scientists to bulb your way to Lib, grab it, and than you've got a super early key military advantage and have denied the AIs one way out of the mess you're going to put them in.
There's obviously a lot more to say about this, but that can wait for your next game. I would recommend you focus on both city micro, worker micro and experimenting with Great People. They
can turn a loss into a win, if used correctly, so it's definitely worth learning how to use them properly.
What is "SP"? Yeah, I didn't look into the captured cities' wonders. I could have exploited all these war spoils but didn't. What is the rationale of switching to Representation after acquiring Pyramids?
"SP", in this context, refers to...a wonder who's name I can't recall off-hand (can't open the game right now) - Swagadon Paya, or something along those lines. It's a wonder that allows you to use all Religion civics without having the necessary techs for them.
The reason why you'd switch to rep as soon as you grab mids is because Rep gives all specialists in a city - free specialists, citizens you're working as specialists, settled great specialists (including Great Generals IIRC), name it - +3

. Basically, Rep doubles the output of your scientist specialists, turns every other specialists into a scientist+, and just generally increases your beaker output massively. You lose Hereditary Rule's +1

per military unit stationed in a city, but Rep brings it's own happiness boost that's frankly good enough when you combine it with it's other bonus. To give you an idea of how huge Rep's bonus is, just take a look at your cities and see how many tiles they have that generate 6

, which is obviously a huge amount. With rep every Scientist specialist is worth 6

, and every city with just a Library can run two of them.
For the record: Police State is great if you're preparing for/in a long, decisive war (the bonus to military unit production and reduction of war weariness keeps your cities pumping out units faster and longer, obviously important). Universal Suffrage, or Universal Suffering as I like to call it, is a civic you'd only run when employing
very specific strategies. Otherwise you'd never use this civic unless forced into it by the UN.
Ok, I'll definitely do that. I'm chin deep into this game enthusiasm-wise and I'm motivated as ever to improve.
Just something I'd like to mention: For as often as we keep saying you still have a lot to learn - and you do, there's entire mechanics to this game that have only been mentioned/glossed over for now, and this game will never even see the latter half of the game's tech tree - you've managed to pick up a great deal of stuff already. You easily could have, say, mistaken Slavery as a trap option and ended up scratching your head as to how people manage to produce enough military to rush an AI so early so quickly, or how people are able to whip out that military without just whipping cities into the ground completely, but you know: 2-pop whips to generate overflow, limit the unhappiness generation and maximize the unit production.