What are the various opinions on the matter? I know this is vague, but I'm really at a loss. My mother claims to have seen/spoken to Eliyahu Hannavi many years ago, so I'm curious on if we believe halakhically that this can be real, etc.
There is a very well discussed literature on the subject of dreams. As was already noted, our tzaddikim have experienced Eliyahu Hanavi, and have dreamed him. It is certainly possible that one could dream about him or dream interacting with him.
However, that being said; we are on a very low-level today, and while it is possible, it is unlikely except for the most saintly - and they probably won't tell you if they did. So what do we do if we dream about him? Well, it is more than likely that subconsciously or consciously Eliyahu Hanavi came up in conversation, or she thought about him. In which case, it is very common for us to dream about what happened in our lives, which can have a profound effect on us.
If indeed she dreamed about him, and there was no connection to what she experienced that day, she should make a note of it and speak to a Gadol to ascertain precisely, if anything should be done.
Since this was several years ago, I would take it as something that did not have a profound effect on her, since she would have gone to a Gadol immediately. I would surmise then, that the dream was probably a subconscious recollection of a past discussion of Eliyahu Hanavi or she read the accounts in Tanakh.
Yes, dreaming of Eliyahoo can be real. Many people see Eliyahoo and many other Tzaddikim in their dreams.
The Halachic implications:
If Eliyahoo appears in a dream and asks you to do Mitzvos - do it (you don't lose).
If he asks you to transgress Mitzvos - don't do it.
If he tells you anything that pertains to money (as if somebody owes you or you owe somebody) - don't believe him (that's the Gemmorah's ruling).
If he says something questionable or unclear - ask a Rabbi.