1) Yes. When it comes to bonus tiles, everything that generates productions points gets the bonus. Or everything that generates research gets the research bonus. Approval bonus gets applied to morale buildings, and so on.

2) Early game - keep morale at 100% (or at least 70%) in order to grow your population. In DA, you start with 5000bc, that should last you a good while (in TA, you start with only 3000bc, making it a lot harder). Anomalies are also a good source for income, especially since they respawn now. You can also try to sell relatively unimportant techs (if you have tech trading on), the AI pays good money for stuff like Universal Translators or Xeno Communications.

Make sure not to research factory / lab upgrades too early, unless you have a good cash flow. By default, ALL buildings get upgraded, which can lead to a drastic increase in spendings if you are not ready for it.

The buildings upgrade when you research the branch of the tech tree. All factory upgrades are in their own branch (Xeno Engineering), same with approval, economy and research. There IS an option to deactivate the automatic upgrades, but it has to be set per planet and then you have to remember to manually build the upgrades. Depending on your galaxy size, it can add up to a lot of micromanagement.

Not sure what you mean about starbase level indicator. Levels are gained through combat only. You can install more influence modules after researching the appropriate branch on the tech tree (Cultural Domination, one of the yellow ones IIRC).

Does the wiki have some detail on asteroids? I have yet to find that page.

A number of players (myself included) use planets for specific purposes - Manufacturing planet, Research planet, Economic planet, Low Quality planet, etc. For most planets, I queue in the following right at the start: 1 Shipyard, 3 Factories, 1 Market Center, 1 Farm. I play as a technocrat so I don't need to put Research into the original queue. The second queue is when the planets start to specialize. Often the planet's specialty will be determined by whatever "special" tiles it happens to have. I have 6 or 7 groups of planet names that I use to assign as needed - Viking names at the top of the map, Mayan names at the bottom, Conan names where I expect danger, and so on. This helps me to locate my planets quickly during a game (when I have 20-30 planets).

Starbases are of critical importance. I use a spreadsheet to list all 5 types of starbases (and their data) on 1 sheet for easy reference. There are 6 "upgrades" for economic starbases (9 if you count the 3 Trade upgrades also). These range from Starbase Factory to Orbital Replicators and require research in Xeno Industrial Theory to Industrial Sector to access them. Ideally you want to put an economic starbase in the middle of a group of colonies that you control (or expect to "acquire"). A fully upgraded economic starbase can increase your productivity 24% per planet. So if you build a clump of 4 economic starbases next to each other you can nearly double the production of each affected colony!

Also (very very important) is to go for as many of the "diamond" resources as you can get. At the begining of each game, my home world builds colony ships - but the first 2 or 3 planets that I colonize build constructors. I use these to acquire resources or build economic starbases.