If you haven't been doing it, adding site:forums.galciv2.com to the end of a search engine (e.g. Google) entry can help you find posts around here better than the local search.
The two expansions include some major additions and changes from the base game, so "good" answers to some of your questions will depend on which game you're playing. DL is simpler, and some folks around here recommend starting with it until you're comfy enough to start messing with extreme environment colonization and civ-unique tech trees.
If you run Vista or have .NET installed on an older OS, you can try the free Galactopedia
app. It reads the XML for the tech trees and provides a GUI to help you poke around and learn about things like Stock Exchanges having a lower maintainence cost than Banks.
Planet improvements: single best advice I have is go slow in adding them; you need to build up your income before you build up your infrastructure.
Ship production speed: more (& better) factories can help here, as can Econ starbases with the right modules added. Rush-buying is very common for players who run huge economies. Starbases can also help research production, as can some trade goods and unique improvements like Nanorecorders and the Tech Capital.
Exploration: the influence zones throw lots of people to start with, especially if you have a strong Civ background. Yes, you can place colonies (& starbases) in another civ's "territory." But you should be cautious about it--if their influence is very strong, you're probably just saving them the cost of a colony ship because the world will flip to them pretty quickly.
I'm unreasonably fond of this game, but have to respectfully admit that I believe documentation is their weakest area. These forums are a good resource--plenty of folks like answering questions. There's also a Galciv wiki