In the American military a warrant officer is a subject matter expert in their career field. They are supposed to be advisors to commanders on the best tactics, techniques, and procedures at most levels, all the way down to the company level in army aviation. They are in most fields of the military like maintenance, personnel, property, aviation, special forces, etc.

Warrant officers in the American military are commissioned officers, so in some instances they can be used as an XO or detachment commander. They usually have limited Uniformed Code of Military Justice(UCMJ) authority, but are just as capable of running a unit as a captain or a major.

In the case of Ridley, rank and position aren't the same thing. Ridley is a warrant officer in the aviation branch, but the third ranking officer after the commander and XO or first officer.

Warrant officers are supposed to be those people with knowledge that is an inch wide but a mile deep about a certain subject, but they are almost always very capable people and sometimes take on more roles. US Army aviation is the worst about this. They use flight warrants as catch all officers and will use them as supply officers, NBC officers, unit movement officers, or really any other job there isn't an enlisted person qualified to do the job.

Most of my experience is US Army aviation, so feel free to take it all with that in mind.

i never got the impression she was the pilot.

not sure where in the hierarchy her role/title would have been, but she was clearly management... handling pay issues, and being very knowledgeable about all onboard systems, policies and procedures. #3 sounds right; behind the captain and the android

Well, a warrant officer is essentially an in between rank. In most militaries, they're one notch higher than an NCO (non commissioned officer) but below a commissioned officer.

Now, if that doesn't mean anything to you, an NCO gets rank through direct service from enlistment at the lowest rank, with a hard limit (during peace time anyway) on how high they can go without extra training. A commissioned officer is usually going to start at the lowest commissioned rank right out of an academy or other training facility. Mind you, this varies even between services, and can vary even more between nations, and is over simplified.

I don't think that the Nostromo was a military vessel at all, so being the warrant officer could have any meaning at all within the context of the film. That being said, I got the impression she was basically the person in charge of cargo and gear used in the work as an exploratory commercial ship. The position as third mate or the equivalent would have been more about chain of command than any specific training the way the military would have. One if those things where the job is dangerous, so the possibility of death is high enough that you want to know who is in charge if the worst happens, but everyone is able to run the ship to some degree as well.

Kane was the SIC/XO for sure, but his job wasn't ever detailed beyond that, which is one of those hand wave things that happens in movies. If the ship was run like the merchant marines, the deck officers (Dallas, Kane and Ripley) would have more specific duties and roles, but I got the impression that the company didn't function like a merchant navy at all, and the ranks were largely applied as a nod to tradition rather than a real world analog.

Outside the movie universe, I suspect that the writer just didn't bother to look into naval rankings, or other sailing ranks and just went with what they liked in the way of terminology.

But I would say that the structure was closer to merchant marines than anything else in the real world within the movie.

All of that stuff comes from second hand info though. I had a few cousins that were merchant marines, and a few family members that held various ranks in either the US Navy or Coast Guard. My grandfather was career Navy, and ended up going from enlisted into officer training and retired as a Commander. So I picked up a bit, but never experienced it directly.

I tend to think of those parts being window dressing rather than world building since it's never given any weight in the other movies.

It's been a while since I've seen the movie, but Warrant Officer is a rank used in several different armed forces. It's exact position varies, but you can think of them as either the highest rank grunt or the lowest rank officer.