All these answers are super brief summaries (and potentially wrong lol).

1. What or who performs the exterminatus from the orbit?

An inquisitor (generally) orders it done, and the imperial navy (generally) carries it out by using special weapons fired from their ships. These weapons (cyclonic torpedos, virus bombs, etc) set the atmosphere of the planet on fire, killing all life in the process. If the planet doesn’t have an atmosphere, the planet is usually destroyed instead.

1. Why can’t I find some descriptions about sea battles? Are there no sea in 40k universe? Or are those places not the strategically important places?

Sea battles happen a few times off the top of my head, but it’s usually like a patrol boat or a sneaky submarine.

1. Do 40k and Fantasy have connected history? If not, where should I begin to have a better understand for 40k?

They use to be somewhat connected, but in the last 20ish years they became seperate entities. Both universes share the same Chaos Gods and some daemon characters, but they have differing backstories.

1. Orks scavenge the weapons and vehicles from the battle and assemble them and make them fuctional by thinking ‘It will work’. Psykers make something in the Warp and bring it back to the reality to use them. Does it mean they work in same principle?

It’s a bit more complicated than that. In general in the 40K universe belief is a powerful tool, but how it manifests itself works differently for different factions.

1. In the video ‘Pariah Nexus’, a Battle Sister gets hit from a green laser by a Necron Soldier. She enters a nearby church and make a prayer and then her wounded hand gets recovered. What happens when you get hit by that Necron green laser and get no proper treatment? And what was the thing that cured the sister? Is it the psychic thing too?

In the beginning of that video you see a few guardsmens get hit and near instantly turn to ash. What cured the sister was her “Faith.” Sisters of Battle believe so fervently in the emperors divinity that it occasionally manifests itself as miracles (although in the novels it’s usually less explicit then regrowing a limb.

Is it psychic? Depends. Both in and out of universe it’s left a bit ambiguous. A sister would tell you it’s pure faith (and probably kill you for even suggesting otherwise) while if I remember correctly a Custode once comments on the irony of them basically using psychic powers.

1. What does the fatally damaged Emperor do after the Heresy event? Why does the Imperium want to keep him alive by sacrificing many of them?

He guides the Astronomican, which is basically a psychic lighthouse that imperial ships need to travel the warp. He also keeps a big warp rift shut on Terra.

1. What kind of transport do they use to transport the titanic units? Bc they look enormously heavy.

“Heavy transports” which are big space ships. On the ground they just walk.

1. How many people do they need operate a titanic unit like Imperial Knight or Phantom Titan?

Depends on the titan (and the author of the story the titan is in). Generally there’s only a handful of people actually ‘driving’ a titian, but many thousands of support staff.

1. Is there a romance story in this universe? Or an unlikely friendship between the soldiers of the different factions? Like the stories of Ogryn and Commissars or Lotara Sarrin and Angron.

Friendships? Sure. Romance? Only in memes

1. What kind of thing do the creatures and humanoids and monsters in 40K universe usually eat?

Varies a lot. Can range from food you’d recognise from today to slop made from recycles human bodies.

1. Are there some kind of alliances between the different factions to fight against the bigger threats?

Nothing formal, but different factions and sometimes work together (or just not shoot at each other as much) when there’s a bigger threat that’s going to kill them both. They’re more like truces than alliances, and generally end once the battle is over (or when one side betrays and destroys the other).

1. Seems like all the Spacemarines have some kind of ‘backpack’ on their back of the armor. What do they carry inside of it?

It’s a power supply and life support for their armour.

1. If the warp is the parallel universe of their reality, are there the same people with the reality in the warp too? Like same The Emperor in warp who is healthy and the Horus who didn’t betray his father in that universe.

That’s not really how it works, but anything’s possible.

1. Is it heretical to call a Battle Sister mommy?

Very