I guess it's probably helpful to know what a rogue trader actually is. I think the game explains it somewhat, but just in case, here's a (not so) quick rundown on some major components of the lore and game.

A lot of people think that rogue traders are just the captain of a big ship. They are not. They command nearly unimaginable power within the imperium. They have a warrant of trade sealed with the blood of the emperor from a time when he walked among men. It is both a holy relic, and a hall pass to do whatever the fuck they want mostly. They are pretty much outside the bounds of imperial law. They can recruit xenos and worse into their crew. They can befriend, dominate, subjugate, and exterminate entire systems if they wish. Not even the Inquisition can really boss them around, but Lord inquisitors are probably the only authority to actually influence a rogue trader. A rogue trader wouldn't want to piss off a lord inquisitor and vice versa.

It is the duty of rogue traders to navigate unexplored space and claim worlds for the imperium. The world's they claim are theirs by right of their warrant of trade, but those worlds are required to pay tithe to the larger imperium, which is non negotiable. The tithe is usually set by the high lords of terra or the administrators that work underneath them.

As for wizards/magicians, they do and don't exist. They are called psykers, and their "magic" is derived from the warp, the nightmarish parallel reality inhabited by daemons and their respective gods. Using warp energy is extremely dangerous, and can cause the veil between realities to thin. If it thins, tears open up, and daemons can burst forth. This is usually a one way street, as anything non-daemon entering, or even seeing the warp, will pretty much instantly go insane, turn into a chaos spawn, or worse. There are very few exceptions, but they do exist. There is a lot more to the warp, I'd recommend looking into it deeper if you're interested. Leutin09 on YouTube is a great source.

Now that we know what both rogue traders are and what psykers are, we can talk about navigators, which are a really important part of the game and lore. They are human, but mutated. They have a genetic trait that gives them a third eye on their forehead. They use this eye to see into the warp. It's not perfect, but it can help ships travel through the warp, which is humanity's form of faster-than-light travel. Pretty much every warp capable craft will have one. Ones that don't take extreme risks even doing the smallest warp jumps. Without navigators, the imperium is screwed. It's why they are one of the very few types of sanctioned abhumans.

As for the mechanicus, machines spirits, and the god they worship, it's somewhat complex. The mechanicus at its height was technologically progressive, and significantly more advanced than the contemporary version. They understood how to create and innovate. During the age of strife, they lost much of their knowledge. Creations they once built, they have lost the knowledge to rebuild, repair, enhance, and sometimes even maintain. When dark age technology is lost, it is usually lost for good, which makes it so valuable. The current day mechanicus has stagnated, and are afraid to progress as innovation has caused problems in the past (see Age of Strife and men of iron).

The modern day mechanicus warships the omnissiah, which is essentially the avatar of the machine god, which they believe is the emperor. In a roundabout way, they do workshop the emperor, which is relatively in line with the imperial creed. The mechanics is technically separate from the imperium per the treaty of Mars that the emperor signed, which gives the mechanicus religious freedoms and rights to technological finds, such a STC fragments. I'm not going to talk about STCs here. Mechanicus likes the fragments. They struck a deal with big E, and now they are an allied faction to the imperium. For all intents and purposes, you can consider them a joint faction, but they are technically distinct.

As for machine spirits, they do exist. I think of it kind of like how orc psychic manifestions work, though, to be honest I'm foggy on the details as machine spirits did exist during humanity's enlightened phase. Technology does have machine spirits, and the more powerful the machine, the more powerful the machine spirit. Tech priests sometimes must commune with and appease machine spirits. Angry machine spirits can cause their host machine to misfire, break down, malfunction, etc. Appeased machine spirits can greatly enhance the effectiveness of the machine they are bound to, with some spirits being so powerful they can control aspects of a machine, such as advanced targetting systems, defensive capabilities, etc.

The last thing I'll touch on is the emperor. Some comments say he's dead, some say he's alive. The truth is that he is neither. He is a husk that resides on the golden throne - a dark age of technology device that is a psychic amplifier and a life support system. It maintains his decript body and allows him to remain in a state of undeath. His psychic abilities are so powerful that he cannot really die. There is a lot more to this, as the emperor is a perpetual. I can expand on this more if you want, but I'll leave it out for now as it's complicated. Anyway, he is so powerful a psyker that he is the focal point or source of the astronomicon. This is essentially a psychic lighthouse in the warp that navigators will use a point of reference to know which way holy Terra is. They also say the emperor wages and eternal psychic war in the warp with the chaos gods, which keeps chaos from taking over the imperium of man.

You've got the gist of the foundation of the lore down, so my breakdown above is a little more comprehensive. Feel free to ask any more questions or DM me. I also wrote all this at 2am in the dark so if there are typos, inconsistencies, or things that need further clarification, I apologize and in advance.