1. I am not aware that government type changes the amount of labs/factories and so on. The only option to changing that is conventional start/trans-newton start.
What the race-government _does_ change is to give bonus/mali to several racial stats.
Open the "View Race Details" window (CTRL+F2)
In the "Government Modifiers" section (lower half, left side) there are stats for Xenophobia, Determination, Trading, Diplomacy, Expansionism and Militancy. Each type of government provides a bonus or malus to those stats, which are then applied to the random numbers rolled for your race (right side, center)
Xenophobia - malus to your relations to other races, applied each year.
Determination - how hard it is, to make a population of yours to surrender and, I belive, also influences how much garrison the enemy needs to keep your conquered population suppresed.
Tading - Influences the income from trade, I belive
Diplomacy - Bonus to your relations to other races, applied each year (yes counteracts xenophobia)
Expansionism - How fast the race explores and expands (irrelevant for a player race, as you deside those things)
Militancy - How strong a military the race wants/supports (irrelevant for a player race) Note: I am not sure, there isn´t something else where militancy is counted. If anybody knows, let me know too
2. All officers (yes, scientists and administrater count as officers for this) are "crated" in the military academy. Which kind of officer is "created" is random with a preferance towards naval officers.
3. Research priorities totaly depend on what race you are playing. Personally, I play the curious explorer and don´t bother with weapons until there is a reason to. If, once in a while, I go the WH40k route "purge the Xenos!" I invest heavily in weapons/warships and go alien-hunting.
What I almost allways do is, keeping 10% of my industry building factories and mines and at least 20% building labs. The remaining 60% build whatever is needed at the moment, automines are something I build very regularly. I also like to have quite a few shipyards, to reduce retooling (If I field, say a CG, CA, CE, JC, then I will aim to have 4 dedicated yards) This also allows for a fast emergency buildup of the fleet
I also keep my top CP-researcher researching "Expand civillian economy" and "Research Rate" all the time.
Money _will_ become scarce, especially with a trans-newton start, so keep researching the economy. Financial Centers might help, but you´d need a whole lot of them, to do you much good (each one generates as much cash as 1 mio colonists would do).
After settling Mars and usually Titan, I am looking for minerals. Look what mineral is going to run out within the next 10 to 20 years, look for planets/moons in other systems, that can provide that mineral. Start looking _NOW_, don´t wait until you have to shut down production because you don´t have any left!
If the mineral goldmine(s) is/are colonizable, so much the better, prepare infrastucture and mines, if not, build automines.
Subsidise the civies, so they build more ships while you have a lot of money, the tax, they will pay might help you later, when cash gets scarce.
Only buy the minerals from civilian mining colonies, where there are a lot of different minerals. You pay PER MINE, no matter how much minerals they recover.
On a moon with 10.000.000 tons of Duranium (1), a single civ-mining-complex recovers 100 tons (basic tech) of minerals.
On a moon with Duranium, Neutronium, Vendarite, Sorium and Uranium at 0.5, the complex recovers 250 tons.
You pay for both the same!
The "sometimes 2 scientists, sometimes 4 to 5" thing:
Thats how the dice fall. Sometimes you luck out, sometimes you don´t. A great thing (IMO) to do is to modify your research priorities towards what you get. If I get a energy weapons genius, but no misisle scientist, my fleet will be mostely beam-armed. If it´s the other way around, it´s all missiles and railguns.
Also remember: Each scientist can research everything. It´s just that he is not receiving the 4x bonus if not working at his specialty.