3. Generally only when needed.
well in singleplayer mode you can research more than what Ryat suggested.. Best things to grab are ship types, ice and volcanic colonization, increase of terran population, first two increases of resource extraction (I am sure someone will complaind many of these are not worth it, but I say especially in single player they do worth it..) and to be able to see incoming enemy ships. Hull upgrades are cool with damage increase (but be warned, they need many ships to be effective, like don't increase laser if only 5 ships use that..)
4. Asteroids are great for starting off as they are cheap to build up. Colonize everything.
I must say the colonize everything part is a bit wrong (but I know the best thing is to grab all possible planets), if you overextend our empire you will get attacked on multiple fronts and take heavy losses.. I say colonize the planets that you can defend with your fleet!! dont build defense structures only when extremely needed, like a chokepoint planet, and never forget to upgrade the first (first two) population upgrades as they will get rid of underdevelopment taxes. Best to colonize are: asteroids, dwarfs, terran-desert if you can defeat the defenders.., Volcanic and Ice are a bit expensive, but if they have 3-4 resource asteroids grab them fast as they can worth more than a terran or desert.. Your capital ship alone can defeat most defense fleets, only the most guarded terran and desert worlds are troublesome (and assuming you chose a medium or strong capitalship as a starter)
5. That is a huge debate. Against AI early to mid game is fine but against a human it can get real tricky.
I would say if you are to think about geting your second capital ship (dont build a second one..) and have a decent economy, like 40 credits and 5-10 metal and crystal income.. You need to have a sufficient enough fleet to defend your empire while your titan builds, but you have to decide what is enough. Against higher level AI-s you need to build a starbase or 2 before thinking about titans.. Titan class warships are sometimes game changers, can defeat small-medium fleets alone, sometimes they go down very fast against a significantly bigger fleet..