If you're waiting for the resolution to any particular request, like a research project or a query, it's perfectly fine to put in other requests at the same time. The limiting factor there is really just my own time and energy, and obviously the more stuff I have in my to-do queue the longer it can take to get to any one particular thing. The only type of request for which there's an actual coded limitation is full personal story submissions, which I think can be done once every 3 months. But smaller stuff is all right -- all I ask is that everyone keep in mind that I am only one person, and I will get to things when and as I can. :)
As far as background events go, essentially anything that happens in the world, whether as in-game happenings or rumors or IC story announcements or whatever else, is something that is available for players/PCs to engage with. They can do this in really any number of ways -- putting in queries to talk to an NPC, investigating through plot notes, RPing with whatever NPCs might happen along, creating their own more personal story arc to go along with some particular aspect of an event, or whatever else. This doesn't mean that anybody HAS to do so, nor does it mean that there's any expectation on the admin side that any specific action will be taken. No one has to engage with any particular event at all (unless of course something directly happens to sweep them in). Nothing that's been happening in Omrazir so far is of vastly earth-shaking scale or urgent in nature, so PCs and staff alike can simply engage with them as time allows.
Also, any given happening may have more natural "hooks" for some PCs than others, depending on their background and the interests they've demonstrated through RP, but there's nothing to stop anyone from engaging in any way that makes sense for their character. I'm also happy to try to help people get involved by working with them to develop a hook that they find interesting. Of course once a PC is involved in things there's no guarantee of exactly what will happen as a result! (I usually don't fully know either.)
From the perspective of thinking of other types of games, it might help to see Avaria as more of a simulation game than a big-story narrative RPG. There are lots of things out happening in the background of the world, some near at hand and some farther away. It's possible for any of them to affect PCs and their personal stories in various ways, directly or indirectly, and it's equally possible for PCs to affect them by reacting to them in any number of (open-ended) ways. Very occasionally some event will happen that's big enough to directly impact most or all of the playerbase, but especially at this point in development that's very much the exception rather than the rule.
So you can pretty much decide how you want your character to spend their time within the framework of the world, whether that's jumping into an existing storyline (either staff-run or PC-driven) that seems right up your character's alley, coming up with your own stories to sweep other people up into, or just quietly doing your own thing with your own more personal stories. Each of these things can definitely have its own personal rewards.