2. While trade usually doesn't rake in huge amounts compared to taxes, it does help. As you already know, far trade routes yield more (with the trade ships bringing in more cash when they are further away on their route); sending them to capitals of other races also helps though I don't know the exact relationship between trade income and the planet's economy. 10 trade ships can easily bring in 500 bc each turn without using any economic starbases
The most important impact of trade ships however is that they improve your relations with the races you establish trade routes with.
3. I typically start with 1-2 factories or similar buildings to speed up construction on a planet. I then specialize my planets, mostly based on any bonus tiles. Many of my planets also end up with only economic buildings and those 1-2 factories in case I need to upgrade my buildings. When I'm not upgrading, I switch their focus to research so those factories contribute a little to research.
Advantages of specialization:
- bigger impact of buildings that give X% bonus on a particular planet (e.g. forge, research coordination center)
- more concentrated output which allows to build unique buildings / wonders faster
- more concentrated output which allows to build large ships faster. I prefer to be able to construct a few large ships in a limited number of turns, rather than having 20 planets in parallel taking a year to build a ship each
4. This is common, depending on your settings (galaxy size, number of planets, number of habitable planets, number of extreme planets). Colonization is all about speed, both producing colony ships fast and researching/adding better engines so they reach their destination faster.
Researching extreme planet colonization technologies only comes in handy once the normal planets have all been colonized and you see a few high quality planets in your area.
5. At the start, I develop my home world to get some early ship production and research going, then I research trade to build an economic capital. My second and sometimes third planet are dedicated to ship production, my next planet to research. Beyond that I colonize but don't build on planets yet until my economy becomes stable or the planet becomes self sufficient (i.e. the additional maintenance cost of an economic building is offset by the additional income it generates). Once my economy is in decent shape, I'll develop some more planets into production / research havens.
6. Don't remember from the top of my head but I believe that's something you can change in the general game options / settings. I know that by default I see the summary view of hitpoints, damage dealt, damage received, etc. at the end of each battle so it must depend on user settings.
7. That depends on personal preference. For small galaxies I tend to go with 2 majors and random minors; for medium and above I go with 3-4 majors and 9 minors. While minors take up a valuable planet, they're great to trade technologies with early on and if you're the one to capture their planet you can end up with multiple economic / research / manufacturing capitals (especially after you've traded the necessary technologies with them, that usually causes them to start building those capitals).
I prefer to have a slightly crowded galaxy since it becomes more active, more close borders and overlapping influence areas mean more chances of wars breaking out.
8. I don't use them enough; military starbases can also be important to boost your military rating so you seem stronger. Some people make heavy use of economic starbases to boost their planet and trade income (but then put enough defenses and weapons on those starbases to make them less vulnerable).
I also use influence starbases in the same way as you do, quite often you don't have much choice if you want to avoid your planets flipping or if you want to pursue an influence victory.
9. Here again I'm not an expert; I let my original miner do its job but I don't know the benefits either. Some people prefer to convert it into a colony ship to speed up their early colonization though.