1.) yup, what LedZeg said
2.) Focus diverts (in DA I believe its 1/3, in TA 1/4) to the selected field. That is, at 100% production, on 100% social production, a world producing 100 hammers, with focus on Research would be 0 Mil, 75 Social Production, 25 Research; even though it doesn't have a single lab.
3.) You can gain passive speed boosts (+1 to speed) once you research certain technologies (Impulse, Warp, Hyperwarp, etc). A ship, with no engine techs researched, with no engines will have a speed of 1. A ship with a single Hyperdrive engine will have a speed of 2. All races starting ships should have at least a starting speed of 2.
4.) Yeah, its a bug thats getting worked on.
5.)Like LedZeg said those are race specific techs that only that race can research. Generally speaking, you want to trade for these techs if you can as they often have passive bonuses that are quite useful or provide an unique structure that can prove to be beneficial.
Anything else we can help you with?