1. My first game I went out really early and got destroyed by an NPR, but that may have been bad luck. My current game I stayed home for 20 years colonizing the worlds in Sol, then went out after I had decent military tech and a small defense fleet.
2. First you have to retool the shipyard to build a ship, which requires it to be at least as big as the ship and the same type (military or commercial).
3. You can't build basic ship components like fuel storage or crew quarters, the shipyard does that. Ship components aren't equired to build a ship but they are REALLY useful. They are used by shipyards, and when a shipyard uses one it doesn't have to build that component - thus shortening the ship construction time. If you build all of the components you can churn out a ship every month or so, instead of every year. It's only useful if you need to build ships quickly and can spare the construction factories to make them, but it's a lifesaver if you're under attack and need ships now rather than later.
In my first game I was in a battle with a hostile NPR and was losing, but using all my construction factories on all my worlds and shipping the components to earth to build war ships let me build a defense fleet in a month that I couldn't have built in a year without the parts. I still lost (my ships sucked and I didn't know how to control them, heh), but I would have lost a whole lot sooner without using ship components.
4. Like they said, mass drivers. You only need one on the receiving planet. One on the others too, unless they produce more than 10k a year.
5. I like Mesons myself, they go right through armor and shields, but are half range of lasers and only do 1 damage. The one damage is instantly internal damage though, which is nice. I mostly use them for PD to shoot missiles and I'll tear ships up too if they come close enough. Long range weapons, missiles are the best.
6,7,&9. Missiles can nuke planets. You can even make them extra radioactive to kill the population faster. The radiation takes time to dissipate though, so a nuked world isn't as useful for a while. If you can afford it, taking via ground forces is easier on the planet.
8. Your governers sometimes have high bonuses in certain things, so you can focus if you get a good governor for something. Like I have some 30% wealth bonus governors on worlds that I use entirely for financial centers to generate money for my other worlds. Research doesn't get bonuses for that, so you can stick it whereever you have the population for it. You usually want to focus labs on the researchers who have the good bonuses. The bonus is x4 if it's research in their specialty, so you can get huge bonuses if you have people in the areas you need to research. I have a guy with 50% bonus in C&P, x4 = 200%. So he produces triple the normal points, and has a 30 lab limit - effectively 90 labs. I used him to get all the research point techs, current up to the 1000 RP per lab (that one costed a lot of points, hah).
10. CIWS are only useful to defend that specific ship from missiles (doesn't help others in the fleet). I haven't used them much, since they're short range - I usually shoot down all the missiles with anti-missiles, and my fleet's mesons mop them up before they get into 10km range.
11. You could build a ship with no engines loaded with a bunch of fuel tanks, use another ship with a tractor beam to tow it into location, and then send other ships there to refuel. You would still have to send ships to refuel it though. Probably easier to make a colony on a rock somewhere and just dump fuel on it, then refuel from there. I think you can just add a colony to an asteroid and not put any people on it and just store stuff there. I haven't tried, though.
12. Like they said, it requires no military components - not just civ engines. Also, about civs: Civ shipping lines will eventually build either colony ships, freighters, or luxury liners (if you designed them). If you don't want them building a certain ship you can set it to obsolete in the design window after you have a shipyard retooling for it. To get them started you can go into the shipping line window (ctrl L) and subsidize them. They spend the amount of money that the ship costs in build points, so if your only freighter costs 6,000 BP then they need 6,000 cash to buy one. Subsidize them to that level and they should construct a ship in a few months.
13. It depends on the ship. If it's really big you might have a failure rate of 100%. That just means something on it will fail every year, but if your maintenance supplies is significantly above the max repair (cost to repair the most expensive component on the ship) you can last a while even with constant failures. You just have to resupply every so often. Maintenance failures aren't necessarily bad, it just consumes supplies - as long as you have the supplies nothing happens. If you don't have the supplies the part becomes damaged and you have to spend more supplies later to fix it.
-edit- I think the the moving time to build thing going up by a day is just an oddity, its all calculated in 5 day periods so if you pass a single day it will adjust it assuming you were going to pass a 5 day next I guess - but if you keep passing 1 days it will eventually hit the 5 day mark and cycle it back. If you just use a 5 day increment it will stay the same, but it doesn't much matter either way - it's just a display thing, the actual construction points left isn't changing.