5. You will notice the build time on normal colonization is very slow. Researching the extreme state allows the planet's production rate to increase to normal (IIRC, if you hover over a planet with the first stage of "genesis", it's production rate will be 50% or something). 

2. I believe it's just "filler" material for the game. The more useful pickups from anomalies are 25 % of tech researched, 500 or 1000bc credits found.

Useless ones are 1bc found, morale and loyalty and soldiering ability increased by 1 %. Some others that I can't recall offhand

7. Never seen the gifting of planets you mention, but usually the minor races have now got access to all tech researched by a more powerful civ and are willing to trade them. I never bother with this as their prices are extortionate !

2. "Ship will become much more lethal after upgrade" random stuff from anomaly. What exactly that means?

This anomaly give the ship experience. Normal armed ships will level up when they win battles, giving them more hit points. This anomaly gives your survey vessel the same type of experience, but you need to upgrade it into an armed design to get any benefit from it.

4. Miniaturization bonuses - how exactly they work? I did try to compare stuff before and after, but most of the time they were of the same size...

Miniaturization increases the point capacity of your ships, while the modules remain (mostly) the same size. Many modules have their size scaled to the size of you hull, so extreme amounts of miniaturization can actually make the size of components go up.

To use numbers I know without looking, a tiny hull starts at size 16. The first level of miniaturization will give it 18, and the second will bump it to 24 - this is the minimum needed to put a construction, mining, or colony module on it, as all three of those modules are size 20.

5. Extreme colonization stuff. Heavy Gravity Colonization is all clear, I can colonize the worlds I couldn't before. But what's Advanced Heavy Gravity Colonization? My first guess was additional workable fields inside the relevant planets. Apparently not true.

As stated above, social/military production on these planets are set at 50% with the first tech, then increases to 100% (equal to a standard planet) after the second. FYI, the same works in reverse; if you steal or buy the advanced tech without the first one, the mechanics work the same.

and as a minor correction:

1. Planet quality bonus: increases the quality of each planet. Planet quality equals the total number of tiles of a planet on which you will be able to build after executing all the terraforming techniques (soil enhancement, habitable improvement, terraforming)

Not exactly. PQ is the number of currently usable tiles - terraformable ones are not counted. If you have a racial 10% PQ bonus and settle a class 19 planet, you will get only one bonus tile - the 10% bonus gives you 1.9 tiles, which is truncated to 1 rather than rounded up to 2. If terraformable tiles counted as PQ you would get 2 tiles.

Useless ones are 1bc found, morale and loyalty and soldiering ability increased by 1 %. Some others that I can't recall offhand

On small maps those are fairly insignificant. On larger maps, where you might get 30+ of each of them, they amount to something useful.

I'm (as Terrans) now in this game with Altarians as the strongest opponent, for the moment I'm friendly with them. But they keep sending scary fleets through my territory to attack the Drengin that are on the other side. I support the Drengin to keep the battle going and the Altarians occupied. I like this type of proxy fighting. In the meantime I'm killing off the weaker players and taking their planets.

To answer your question: you can see where ships are heading by clicking on them. i'm not sure if you have to spy on the race first. In addition there's the fog of war. So it might be worthwile to invest in some sensors and put them on a couple of scouts to keep your borders checked. Good luck and post any further questions or game experiences you would like to share with us.

Question from my side: I've the Arceans on my side who I dont' want to attack yet. But they keep building these annoying influences starbases in my territory. Is there some way, besides going to war, to stop them doing this? They have 3 of them close to Earth.

Maiden, thanks for the tip! Unfortunately they are not at war with anyone. They have the highest diplomacy rating

One of the tricks to win a suicidal warfight. Actually people are complaining about the AI's advantage of knowing where all the resources are, but actually, this advantage becomes the players advantage when you use tricks like this.

Let the AI find all the resources, but in the end you be harvesting them!

You can even refine that trick by surrounding that single Fighter with other ships, and leaving only one entrance open which would be blocked by that base. The Fighter then had no other option as to destroy that base in order to get free. Sometimes it won't work though as the gifted Fighter can lock-onto another target (usually an undefended planet) without end.

GJ, don't know if those bases are a real problem to you, as, at least to my knowledge, the AI will never max theri Influencer Bases out and thus, no planets will flip - and surely not your civ cap. And, without destroying them theb these 3 bases are there. But you can prevent the AI from further building any SB by building a one-constructor base (Mil or Econ) and gifting it to the Arceans. It must be in the same sector as the other 3 bases - the AI is also bound by the "max 4 bases per sector"-rule.

Wow guys after a few days with no replies I assumed the forum is kinda dead and never came back until now! My bad

Thanks a lot for your answers!

@Maiden, can you really get only 4 starbases per sector? I never knew this. I guess I never tried this before.

Yes, it's true. And because of this, the maximum number SB's in a Military StarBase Array (MSBA) is 24.

I have tried to search for methods to circumvent this many many times, to no avail. Even if you try to gift a starbase to an AI in a sector where he already has 4 bases - the game won't allow it.

If somebody here ever encounters a game where one player has more than 4 SB's in a sector - well... I'd like to know how this could be done

How do I build a military starbase array?

Is there a way to turn off Dread Lords in Milky Way scenario?

Oh and one more question. It seems that preconstructed ships usually are better than anything I can do myself. I.e. at one point I had battle axe with 10 beam attack 1 shield defense - while I myself couldn't fit even 10 beam attack on the very same middle sized hull. Am I missing something?