Can this verb also be used in some circumstances to basically just indicate location without much reference to posture, maybe for more abstract things that don't have a physical posture the same way that elephants or furniture do? maybe as in these results https://www.google.com/search?ie=utf-8oe=utf-8q=%22Resultater+*+ligger+her%22+site:.no (about results rather than elephants). or are abstract non-objects still seen as having a specific ability to lie or stand? does the word order ('ligger her' or 'her ligger') possibly make a difference in which sort of meaning it could have?
It's often used for files and information on computers, hard drives, memory chips, websites. And also when describing the location of buildings, even if one could argue that they're actually standing.
It can be used with some abstract concepts, but it's mostly limited to cases where you're actually likening that concept to something tangible, as well as to a few common expressions:
"Mørket ligger som et teppe over byen."
"Det ligger mye kunnskap bak denne avgjørelsen."
"Situasjonen ligger ikke til rette for å..."
"Vår største utfordring ligger i å..."
As for the "her ligger" vs "ligger her", I'd say that "ligger her" is used when describing the general location of something you can't see (because of distance, not abstraction), while "her ligger" is used when you could point to whatever you're referring to; either because it's in your field or view or on a map. "ligger her" would still be a viable option in those cases.
"her(/location) + ligger" can also be used to make a statement seem a bit more lofty or dramatic, much like in English. That's what's giving people the "funeral vibe" from the elephant sentence:
"Here lies/rests the greatest man who ever lived."
"In Africa lies the cradle of humanity."
I struggle with the difference also, but the key thing is the context, and I am more likely to make the mistake if I am in button pushing frenzy or in need of a break. Although it does have some issues, I find it very useful to have Google Translate open now, on a PC. Press the microphone once and it repeats at normal speed, press again and it slows it down. Although the accent is different to Duolingo, I can hear the difference now.
They are very similar. Simple answer: You just have to train your ears.
Slightly longer answer: Context is often a very good clue, and can help you distinguish between minimal pairs like this. And to be technical, both a and æ are open, unrounded vowels, but a is a back vowel whereas æ is front.