Here are some actual answers to your specific questions:
Everything is a massive pile of symbols the meaning of which is completely unexplained. The tooltips don't help because they just list off a bunch of terminology that is still completely uneplained.
Page 12 and 27 on here will explain some of those symbols: http://cdn.akamai.steamstatic.com/steam/apps/226860/manuals/GC3Manual_v103.pdf?t=1432646382
The build menu is insanely large, with almost no ability to sort or cut down the list, and is filled with things whose functions I can't figure out.
The build menu in the beginning will have two different kinds of projects: buildings which have a number of turn next to them. That's how many turns it will take to build them. Projects are persistent items you use that provide small bonuses to research, influence, income, what have you. They are produced into perpetuity (unless you tell them to stop) and are usually what you do with a planet when you have nothing you want to build. There is also a military production project which redirects your planet's manufacturing capabilities to the shipyard that planet is sponsoring.
There seems to be a difference depending on where you place buildings, but I have no idea how it works. Also seems to be some system for opening more space, but again...
Broadly speaking, your planets will produce five capabilities: research, manufacturing (both social and military), wealth, influence and food.
- Food is arguably the most important as it provides the baseline for all the others. The amount of food your planet produces dictates the max population of your planet. That max population equals, plus or minus some race abilities and techs, your raw production. All other productivity is a function of that raw production. Max population is raised by building farms
- Research is enhanced with research labs. For research, manufacturing and wealth, you take the percentage of your total expenditures devoted to research and that's the percentage of raw production devoted to research. So, let's say you've got your global wheel set so that research is set at 40%, manufacturing at 40% and income at 20%. Further, let's say on Earth your raw production is 10, that means you'll produce 4 points of research, 4 points of manufacturing, and 2 dollars worth of income from that planet in a given turn. Research labs give you a percentage boost. So let's say you 2, each producing a 25% bonus (for 50% total), you would be looking at 6 points of research - 4 raw plus 50% extra from the labs. Now, when placed next to each other, like buildings raise each others "level," usually to the tune of an extra 5% per level. So, if you put those two research labs next to each other, they would actually produce a 60% bonus
- Manufacturing is enhanced with factories and is split between social (buildings and projects) and military (ships). When you look at the global wheel, you will see a percentage of your manufacturing you're devoting to colony improvement (social manufacturing) vs. ship building (military manufacturing)
- Income is enhanced with markets and pertains to how much money your empire produces
- Culture is generated from consulates and pertains to how quickly your borders (sphere of influence) expands and how likely enemy planets are to switch allegiance to your empire.
In addition, there are buildings that increase happiness (which gives productivity bonuses and prevents uprisings), trade income and tourism.
Opening additional spaces is accomplished via techs along the "green" tech line.
Ship building can't possibly be as slow as it seems to be, so I must be doing something wrong.
You probably have your resources split in such a way that you don't have a lot of military manufacturing devoted to your shipyard. Specializing planets is key in this game. Rush build a couple factories and devote more resources to manufacturing and you should be pumping out ships much, much faster.
Ships have a range limit, which I can't figure out how to extend.
Two ways: (1) new colonies and starbases automatically increase range and (2) if you go to the ship designer there are modules you can add to increase the range of ships so that they can venture farther away from the closest starbase/colony. All ships have at least one or two of these modules by default but you can remove some engines or weapons to increase the range further.
What are the differences between weapon and defense types? Not explained.
In general, missiles are effective from long range but often miss, kinetic weapons are only effective from very short range and almost never miss and energy weapons have a medium range and miss less often than missiles. Each has a commensurate defense - point defense/chaff effectively neutralizes missiles, armor effectively neutralizes kinetic weapons, and shields effectively neutralize energy/beam weapons. Each weapon is also associated with a resource that can be mined which produces a better version of a given weapon - durantium produces better kinetic weapons, anti-matter produces a better missile weapon and elerium produces a better energy weapon. It should be noted durantium is much, much, much more common than the other two and anti-matter is somewhat more common than elerium.
What do all these techs do? How do I figure out what to research?
This is too big of a question and part of the joys of learning how to play the game. In general, I like focusing on stuff that increases my population (better farms) and makes them happy (entertainment) as quickly as possible but that's just my play style. There is no right answer on this one.
Resource information? I'm not even sure what is and is not a resource.
Hopefully I've answered this above. Write back if it didn't help.