1. The tech tree is friggin huge. Or maybe it just looks that way all zoomed in like that, and because it's so slow?
2. I don't know how many planets is "good enough" so I can stop building/buying the colony ships? I had seven in my last game and I bet that's pretty sad on a huge map.
3. Things take forever to build. Apparently, population does NOT matter, only factories. Also, taxes do not matter, either. No matter how much you tax everyone, the limit is based on the number of mp listed in the planet's summary. For this reason I don't bother to overtax people and try to keep morale at 100%. Production is always at 100%.
4. (cont. #3) Manufacturing/research/economy techs keep adding newer improvement buildings, and so colonies are always building/upgrading crap. There's no way around this as far as I can tell, and so this really wrecks your economy, and I spend more time doing this and ignoring military (makes me nervous, but I can't stop myself). There wasn't a single damn turn I spent NOT building something, everywhere. The sad part is, even my class 19 manufacturing plant with mostly factories, a manufacturing capital and a power plant took so long to build, it was literally six hours or real time (maybe 8?)... it had something like 71 social/military in the end before I quit.
5. I forget what I was going to say? I'm so tired...
I just need more help. Maybe someone could tell me how to use starports? And how to get planets improved more effectively? Everything is too friggen slow...
1-Most of the entries on the tech tree are just better versions of a previous one, and nothing really game-changing. For example, there's 5 Laser techs, but the last four are just slightly better versions of the first one. This means the tech tree really isn't quite as complex as it seems at first glance. Even in Dark Avatar, there's a lot of redundancy: all the Laser techs might be in the same block, but the Plasma techs one block over are all still, essentially, somewhat better ways of shooting ray guns at people.
What you can do is to look at the list of researchable techs in the upper-left, and change them to be organized by "category". This will place all the weapons techs next to each other on that list, all the diplomacy techs together, etc. Then if you want to see what you can get later, you can click on one of them and the tech tree viewer in the bottom half of the screen will automatically center on that tech, letting you see what it's a prerequisite for.
You can also zoom out using the mousewheel if you like, but I prefer the method in the previous paragraph.
2-First, you should try not to buy many colony ships. I might buy one or two just to kick-start things, but colony ships are
expensive that early on, and you really need that money to keep yourself afloat until your economy gets going.
As to number of planets, a decent rule of thumb is to get as many as you possibly can. There are exceptions, of course, but in general, the more planets you have, the better off you are. Even if you leave the planet empty because you can't afford to build anything on them (which I typically do quite a bit with the crappier planets), I'd rather have them available for development rather than having to take them away from the AI later.
Just for the record, letting an AI have a planet for you to later conquer can be a good idea on later difficulties, but few players go that high up

3-Keeping production at 100% is good, so you're doing well in that area. However, population matters a great deal: all your production buildings essentially turn money into "stuff" (i.e. production, research, etc.), and population is what provides that money. The more population you have, the more money you get. Keeping morale at 100% is a good way to get more population, since your population grows at double its normal rate when at 100% morale. However, if you run low on money and have to raise taxes, try to raise them until morale is just over 40% on your most unhappy planet, because the way morale and pop. growth interact, anything in between is wasting money.
For production, the first few buildings on a planet should be factories of some sort. You need those factories to build all the stuff that will go on the planet, and you can always replace them with other things later on if need be. If the planet is in an improvement-building phase, have it focus on social production, to speed things up a bit.
4-I try to research that sort of stuff in bursts: pick up two or three trade center techs so that I only have to upgrade once instead of several times, for example, and do one massive round of upgrades then focus on stuff like weapon techs and whatnot. I also don't hesitate to use lower-tech versions of buildings (especially factories) if them getting done quicker would be beneficial. Additionally, make sure that your factory techs are at least reasonably close to what they're having to build: basic factories are going to take forever to build Stock Markets or VR Centers, so I'd much rather have Enhanced Factories or Manufacturing Centers available before topping tech lines like that.
Another thing to remember is that money is all-important in this game. I have enough economy-centered worlds - nothing but farms, morale buildings, and money buildings (1 farm and 1 morale building per planet in DA, roughly 1:1:1 ratio of the three in vanilla GC2) - to fund everything, so that constant upgrading won't crash my economy. These planets in turn fund the upgrades, as well as my factory-covered shipyard worlds and my dedicated research-worlds.
As to your specific complaint, what was it that took so long to build? My money's on Industrial Sectors, since those are so absurdly overpriced, but I could be wrong. At any rate, I might be able to give some specific pointers if I knew what it was took so long to get done.
5-Starports are what build your ships. I like to have some worlds with nothing but factories, power plant, starport, and possibly my manufacturing capital churning out my military. If you meant starbases...I've had a hard time using them very effectively on Huge maps, just since there's so d*** many planets to try to pump up. I'd try identifying a clump of worlds that produce a lot of shipbuilding and research and cluster a few Economic starbases to cover them and pump up their production.
To improve planets more effectively, I make the first few things I build on any planet, regardless of its PQ and what I plan to do with it, be factories. Relatively low-tech factories, at that: Industrial Sectors are hideously overpriced and will take literal in-game
years to build on a new planet, and Manufacturing Centers are also a tad overpriced for my tastes for most new colonies, so I usually give Enhanced Factories the nod. Once those are queued up, I set it to focus on social production and:
--If the planet is an econ world, queue up its farm(s), morale building(s), and econ buildings after the factories.
--If it's a factory-world, queue up the rest of the tiles with higher-tech factories (after the initial factories, so by that point it'll have enough industry to get them built) and a power plant, and later come back and set those first few factories to upgrade to better ones at the end of the queue. When I feel there's sufficient industry on the planet to do so, I start up some ships in the starport and set it to focus on military.
--If it's a research world, after the factories I queue up research buildings (on the +Research tiles first, of course) and a research coordination center, then eventually come back and set its focus on research once I feel it has enough stuff built.