Interesting question for sure, and I would like to add some perspectives that I feel other answers do not cover sufficiently.
Are there fundamental epistemological differences between demons/angels and humans?
I think this is at the core of your question. A related concern which I feel is helpful to the answer is the difference between belief in the existence of God and saving faith.
1. Demons are supernatural beings
This has been covered fairly well by other answers. But to add a few Scripture references (probably not exhaustive): it seems that whenever Jesus encounters demons (devils (greek daimon and derivatives), unclean/evil spirits), or someone else mentions His Name, they know Him and his position (which is hidden even to the people around Him).
Matt 8:29/Mark 5:7-8/Luke 8:28-29, Mark 1:34, Luke 4:41, Acts 19:15
The assumption is that God (and Jesus at least before His incarnation), the devil and other demons would have knowledge about each other due to their supernatural nature. (Also see e.g. Luke 10:17-18, John 8:56-58 for some hints in this direction.)
2. Salvation by belief in Jesus is available only to humans
This seems to be the central theme of the Bible: the fall and restoration of Adam's descendants. The book of Hebrews paints (with quotes from the Old Testament) Jesus (the Son of God) as superior to angels (serving spirits) (Hebr 1) and then calls the saved humans His brothers (siblings) (Hebr 2).
Quote Hebrews 2:16:
So Jesus helps Abraham's descendants rather than helping angels. - God's Word
For of course it is not with angels that he is concerned; instead, it is with the seed of Abraham that he is concerned. - Unlocked Literal Bible
For surely his concern is not for angels, but he is concerned for Abraham's descendants. - New English Translation
This of course assumes that demons are of similar nature than the angels spoken of here. What applies to (good) angels applies even more to (fallen angel) demons.
Furthermore, 2 Peter 2:4 seems to indicate that those fallen angels have already been "found guilty" and only wait for sentencing. Again, assuming these are the same as the demons mentioned elsewhere (which do, in some of the previous references, speak of a certain time they will start undergoing punishment), but leaves open the question whether "hell" and "chains of darkness" still allow them to roam the earth as we perceive it.
I believe from the foregoing that there is no plan for salvation for the fallen angels/demons as they have been found guilty already.
3. Uselessness of demons' faith
Evangelical theology has the central tenet that we are "saved by faith" (as opposed to following the law). Rom 4 expands on this on the basis of Abraham's faith. But, as the section from which you also take your verse, Jam 2:14-26 shows, simply believing in (the existence of) God is a dead faith that can not save (verse 14). People need to act on that which they say they believe. Demons/evil spirits' acts are evil/destructive by definition when they afflict people, so I would argue that shows the nature of their faith.
Some other verses that come to mind regarding acts following faith, are in Acts 2:37-38 when the fresh believers ask what they should do, and Peter tells them to repent and be baptized (the same pattern repeats multiple times in various forms throughout Acts). Also Eph 2:8-10 contrasts the two kinds of works nicely.
As to atheists, 2 Thess 3:2 tells me that not all people have faith. My experiences with atheists have left me with the impression of the recurring theme that they won't believe without proof of God's existence. Do you see the irony? If something is proven as fact, there is no need/place for faith any more John 20:27-29, Rom 8:24, Heb 11:1. And I agree with the evangelical stance that salvation comes through faith, because this is explained in so many places in Scripture. I don't know why God chose to do it that way, although I certainly can speculate, but that would seem to make it unlikely that people would gain either saving faith or have time for good acts at the end-time revelation of God.