Each planet has a certain built-in influence, which varies. But high-quality planets tend to have a better base influence. You can see this on the planet screen by hovering over the influence number, a tooltip will pop up.
Influence starbases can be used to combat enemy influence. You can build four starbases in each sector which should be more than enough to get the planet out of danger as far as revolt is concerned.
To build a starbase, you just move a constructor ship to any place that isn't already occupied (for influence starbases, close to your planet is best if you're trying to fight enemy influence) and use the Construct button.
Planetary influence is also affected by planetary population, your influence ability (from your race's natural scores or from mining influence resources) and your civ's overall influence on the galaxy. This means that as you expand your empire, your influence snowballs.
Earth (and other Civ capitals) always have a lower approval because of a higher maximum population. As population grows (and a colony becomes more overcrowded) it becomes more difficult to make the colonists happy.
You can give them a tax break or build more advanced entertainment buildings like virtual reality centre, but that will only alleviate the symptoms of unhappiness. There is at least one building which directly affects base approval, but you have to research Xeno Ethics first.
However, one sure way to improve approval on an overcrowded planet is to build troop transports and watch the population get shipped off to fight in whatever wars you have going. Your tax income from that planet will be less, but by the time you're building transports you should have a healthy enough income to compensate.
Low approval usually only hurts population growth (very low approval can result in population decline) and your political party's re-election chances. If you're running an Imperial government they don't get to vote so you can tax them as much as you need to, they won't revolt.
Approval-based population growth is per planet, yes. 70% or above is what you want to shoot for if you can't get it to 100%, but bear in mind there are other ways to improve population growth, like the Recruiting Centre or a Fertility Clinic.
