1) Factories create production points, but the number of usable points is split between military and social production. (Military is for ships being built on the ship yard, and social for buildings on the planet). Furthermore, the number of points is partially determined by your tax distribution. By default, your taxes are split amoung military, social, and research production. To increase production globally, you can increase the amount of taxes or the usage percentage (set at 66% at the start, means that 34% goes to your treasury).

On each planet, you can also focus on one of the three areas to redirect a part of the other two to that cause. It's good to focus on social when building trade goods or unique buildings or focus on military when building an essential ship.

2) Money comes mostly from taxes and trade. The more population you have on a planet, the more taxes it reaps. But high population planets also have issues with approval, so an income planet would need entertainment buildings in addition to farms and economy buildings. Setting up trade routes via freighters is a good way to make money too. Send them to a high-pop alien planet, and you'll get money from them every turn. Also, raising taxes will bring in more money (at the cost of approval) as will lowering your spending percentage. Mining ecomony resources or researching higher forms of government will also raise your income.

3) Yes, more pop = more income but lower approval. Approval affects higher government elections as well as birthrate, so it may or may not matter to you.

4) Increase birthrate by having high approval. >= 75% approval get a 25% reproduction bonus, and 100% approval get double growth! Keeping planet populations above 2.5billion helps keep growth high too.

I've been doing a lot of work on the GalCiv Wiki. It may help answer some questions too.

Paladin thanks for the clarifaction, I knew about Aphrodisiacs but didn't know if there were others. Yea by the time I get around to Habitat Imporvement most of my worlds populations are near or at max anyway, however I still build any wonder or trade good I can, even if they arn't usefull to me, if for no other reason then to deny it to an AI race.

You get money from trade centers, advanced trade centers,
banks, and then the biggie--stock exchanges. If you
have a lot of the latter, you roll in the money and your
morale goes up a big chunk.

At the beginning of the game, I send around survey ships
looking for anomalies that sometimes bring in money. This
is kind of hit or miss. But if you find enough anomalies,
you are likely to get some with chunks of money. That can
help in the early game.