Is dependent arising meant for us to understand the arising of suffering -- or is it also meant to describe how phenomena in the outside World arise dependent on other conditions
I don't think that's an important difference -- not a valid duality ;-)
-- I think that understanding that worldly phenomena are dependent (i.e. empty of self-existence) also helps to understand the arising of suffering.
If you imagined that something "really exists" then you might imagine that suffering too was one of its real properties.
Whereas instead it might be good instead to see that everything about the phenomena -- including whether it really exists, what it really is, and whether it's really desirable or dislikable -- is empty.
See also What is the purpose of the Mahayana 'emptiness' doctrine?
You might get a hint of that -- not believing that something really exists -- in this answer (which I assume is Theravada):
... the conclusion I make is that it's not that Buddhists believe in rebirth, it's that we don't believe in death - the latter being merely a concept ...
Theravada, Mahayana, Vajryana and Tibetan Buddhism -- are they non dual or not?
The Pali suttas seem to me to be full of dualities -- e.g. it describes:
- Right and wrong views
- Skilful and unskillful actions
- Fetters and liberation
- Wise and unwise, noble and ignoble, virtuous and not
Some of the "unanswered questions" seem to me to hint at a non-dual approach to some topics --
They include a waring that "there is nothing" is a wrong view:
And how is right view the forerunner? One discerns wrong view as wrong view, and right view as right view. This is one's right view. And what is wrong view?
'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.'
This is wrong view...
I don't know about Mahayana, I guess one of the more famous quotes from that literature is,
Qingyuan declared that there were three stages in his understanding of the dharma: the first stage, seeing mountain as mountain and water as water; the second stage, seeing mountain not as mountain and water not as water; and the third stage, seeing mountain still as mountain and water still as water.
The little I've read of Tibetan/Vajryana for beginners seems to me one-sided -- it emphasises what I'd call "positive" mental energies (e.g., determination, gratitude), and maybe only characterises the mind as "pure" and so on rather (instead of e.g. "defiled").