Hey there! I have answers to some of your questions.

• About Academy quest, it asked to explore a number of atmospheric curiosities, and after that orbit three systems. I did nothing of that, but Academy was unlocked. Is this a competitive/cooperative quest (regardless GDD update says it shouldn't) or merely a bug?

The Academy's on a system somewhere in the Galaxy. When ANY player finds it, the Academy unlocks and start generating points towards the next hero. Not sure what the interaction is with an existing Academy Quest, but there's that!

• About curiosity system. At game start I found lots of planets with curiosities to explore, but as time passed and found other factions, I found anomalies, or systems without curiosities. Are this curiosities only explorable by first player who meets them, or are supposed to be explorable by all players like ruins in EL?

The Curiosity System is exactly like the goodie huts of the Civilization series (not sure about the ruins of EL); first come, first serve. I have had the AI pass by my systems, and I'd watch in regret as they launch their own probes at some of the anomalies in my systems...

• Said in previous post. On ship design screen, I heard in a video (not sure if PANCZASU or The-Cat-..) that some weapons are best against armor and others against shields. Seen no clue about it in tooltips or any other place. Still the youtuber knows it. Can you explain it somewhere in a clear fashion?

In the ship design screen, when you mouse over a Weapon, you'll see it has a specific "Weapon Type". Example: Your starting Basic High-I Slugs are of type "Projectile". 

When you mouse over your various defenses, you see that some of them will have a line in there about "[Type] Defense". Example:  Your Basic High-I Plating has a line in there about "Projectile Defense".

It's assumed that these Defense types provide a bonus in resisting damage of the type listed in the tooltip.

• Can't clearly see the limits of constellations. I see the names when looking from afar and have an idea what systems they contain, but found no way to know exactly which system are in which constellations and see this from near (more or less when you have about 4-5 systems in your screen).

I could be wrong about this, but I thought that constellations were systems that were directly connected together by Warp Paths (as opposed to systems that required you to launch a probe to find, and would require "Free Movement" to reach). You can also zoom out the map-view with your mouse wheel and if you do so far enough you'll get actual text names appearing to show you the names of these constellations.

Thanks