12 or 13 starbases around one planet? I've never managed more than 4. Still, in my current game I have hundreds of those obnoxious structures.
The key is in how you arrange the starbases. At the default effect radius of 5, you can have up to 5 starbases influencing a single planet if you build all five at maximum distance from the planet. This will prevent you from increasing the number of starbases influencing the planet when you gain access to the area of effect radius increasing modules later in the game, however; there are two such modules, and they each increase the radius of the zone of effect by 2 (so 7 with the first module and 9 with the second). To get the maximum theoretically-possible constellation of 12 starbases at default maximum zone of effect radius (9 tiles), you have to put three starbases three tiles from the planet you want to cover, and then you have a choice between fitting a further three starbases in a ring six tiles out and the remaining six in a ring 9 tiles out, or fitting all 9 remaining starbases into the ring 9 tiles out from the planet you want covered. There's a thread or two around somewhere with images depicting starbase locations for constellations of 12 covering a single point, if you're really curious, but I don't really feel that it's worth the bother.
Military stations are special and get an extra 4 tiles on the radius of the area of effect and so can increase the total number of starbases influencing a single planet beyond 12.
Alien Cultural Trash -20% (what is this?)
The product of the colonization event decision.
Noble +50% (not sure what this is)
Fifth trait in the Affinity branch of the Benevolent tree (the branch that starts with Elevated).
Does this mean approval will rise as population goes up? (I don't think so.)
Actual approval rating will only increase with increasing population as long as the total morale bonus of the planet is negative. However, a negative overall morale bonus can never produce a positive approval rating however large the population grows, and any actual approval rating less than 0 is in effect an approval rating of 0. It therefore does not matter* that increasing the population will increase the actual approval rating of a planet with a negative morale bonus; the effective approval rating of the planet cannot be changed in this way. Also note that if the overall morale bonus is positive, increasing population will reduce approval as expected.
*Sort of. The approval penalty to production is actually kind of weak, and it's entirely possible for it to be better, at least for maximizing overall output, to just accept the approval penalty and build more farms or factories/labs/markets instead of building entertainment centers, especially if you've built multiple economic starbases around the planet or have built one or more of the handful of improvements that provide a bonus multiplier to the planet's production, as these things provide a bonus that stacks additively with the production penalty from low approval.
Overall, the planet looks like it should have
(5 + 4 + 3 + 1 + 10 - 24.8) * (1 + 1.6 + 0.5 + 0.1 - 0.2) = -1.8 * 3 = -5.4
morale, which is exactly what you say the game tells you the planet has. Approval is the ratio of morale to population ([morale] / [population]), bounded between 0 and 1 (expressed within the game as percentages, so 0% and 100%).