1) There are certain thresholds in approval that give you an increase in population growth rates: 100% approval, 76% approval, ... Note that this effect plays for individual planets, so if your overall approval rating is 99% but there are planets with 100%, those planets will get the pop growth bonus.
Below a certain approval rating (41%, not sure) there is no pop growth. Below a certain approval (26%?) your population starts to drop.
Especially early in the game, try to go for 100% approval as long as economically possible so you have a fast pop growth.
The other factor to keep in mind is that you want to win the elections if you're using an advanced government type, so there your overall approval rating is important.

2) Yes, the colony view works really well, I also started using this more often now that I play on large or huge maps. Not using many of your planets will hurt you, especially as of painful difficulty.

3) I prefer a variety, because that way I'm pushed to keep up in all aspects of the game (colony rush, research, military)

4) General trick 1: early on, develop only a handful of planets;  colonize others but don't build on them until the population has increased: building on too many planets at the same time will drain your funds. Once you have a decent population, fill some low quality planets with econ buildings. Once you can afford it, develop the other planets as well.

5) General trick 2: spend some money on espionage once your income is positive; early spies are cheap + you avoid those nasty events such as 'you insulted XYZ ambassador which could have been avoided if you had some spies'

6) Keep ahead in the military race - or expect some AIs to declare war on you. Getting good diplomatic relations (trade routes, ethical alignment, alliances, etc. all help to achieve this) and paying 1 race to attack another may help to avoid having AIs declare war on you, but often it's best to simply have a higher military rating...

7) Tech trading is key if you want to keep up in research. Especially minor races are great for this: giving them some of your own technology in return for their tech (or cash early in the game) doesn't make them much of a threat. Just never trade any diplomatic techs (or your next round of trading will become harder) or too strong military techs (hull size, weapons, defenses, miniaturization)

Incredibly helpful posts, Thank you!

Another question, how do I get cool metaverse badges to pop up in the forums as I earn them?

Disagree, to an extent.  No need to wait till your income is positive.  You can rest assured that everybody else is doing just that, which means that if you can get that first spy out the door ASAP, he can cause some trouble for a LONG time.  I think the first spy costs like 100bc.  That one guy can gather a lot of intelligence.   You should see what happens when you attain Medium intelligence early on--you can see their ships' autopilots going into the fog.   That means there's something interesting in that fog.  Good information to have.

I always have negative income for a while in the beginning.  Can't afford to buy spies early on.  As soon as I have positive income, I put money into espionage.

Military rating has the most effect on score.  Get it going early and work it throughout the game.  MV games are pretty much all about that.  Overall population is also a good scoring point.  Run higher populations on higher PQ planets that have room for extra entertainment buildings.