The game does a really good job of backfilling information as you need it. Hover your mouse over any highlighted word and it'll give you a short wiki entry. It's a very approachable version of the setting.

The big stuff to grok right out of the gate is really just this:

• The Imperium of man is explicitly fascist. They're not the good guys, but no one else is either. There are good people within this world, but there's no "Hero" faction. Everything you see extolling the virtues of humanity in the setting is just imperial propaganda and hagiography, and you'll pretty quickly start to see that play out within the game.
• You've pretty much nailed how Rogue Traders work. They basically act as the frontier of the Imperium, to the point of being allowed to colonise whole worlds, which they then own. Each Rogue Trader family is basically a noble house.
• The Adeptus Mechanicus understand the how, but not so much the why. So, they know how to repair a generator, but they believe that the process involves channeling the "motive force" through the wires. Most of what they do is carefully practiced methodology wrapped up in ritual. This isn't true across the board however; at the higher levels of the mechanicus you do get people who actually know how to do real science. They're just very rare. It's mostly the guys who are like 10,000 years old.
• As mentioned by others, the big foundational thing is the Horus Heresy. Half of the space marine legions turned to the worship of the gods of Chaos, and tried to overthrow the emperor. It's kind of both super important, and actually pretty irrelevant. Like, there are something like 40 fiction books detailing every moment of the heresy, but it's impact on the setting now mostly just boils down to "This is why the emperor is a corpse on life support and why there are evil space marines."
• Because of the warp, a realm where the line between imagined and real ceases to exist, there's a lot of "Well I guess this might as well be magic" in the setting. Gods are real. Demons are real. People with the ability to wield magical powers are real; they might be called sorcerers and witches, or they might be called "psykers" depending on who you talk to, but it's all the same stuff; pulling power from the warp to alter reality. This "magic" underpins a lot of the setting. People with warp abilities are necessary for long range communication and FTL travel.

If you're familiar with Dune or Foundation you'll notice that the setting borrows liberally from both properties, which give you some solid points of reference to draw from.