Nicely observed and elaborated, thanks. I still can't seem to wrap my mind around a couple of scenes. One, Why are/is the two/one boy(s) alone in the mother's absence, and two, the lady tries out the mother's robe in one of the scenes and it is a little too big for her, her losing weight by dint of the mental and physical troubles could be a potent indicative but the dress still looked relatively big.
The roaches could be synonymous to bad memories crawling out of crevices in a troubled mind which E very religiously tries to contain within an air tight box.

This is more or less a response to sheoshaktishukla, but I suppose is relevant to what everyone has written; my posts never end up where I mean them to, anyway, dammit. Plus I have questions at the end to which I'd love answers. So, my take.
I think that it was Elias's real mother (Mutter) all along. I did think for a while that she may have had a twin (as they run in families, plus creep me out, so my mind just goes there) from whom she'd been estranged, at least to some degree. E either didn't know she existed, or she was rarely mentioned, and perhaps only as a sister so as to make their lack of contact more understandable (to another twin.) So there's some sort of accident; Lukas dies, the mother survives long enough to reconnect with her twin, who agrees to take her place (both knowing she'll die) to spare E the additional guilt of having somehow caused her death as well - just as you theorize. She had plastic surgery perhaps to look more like Mutter, but in any case so that a slight difference in his "mother's" appearance post-bandages would be more readily accepted by E. But I decided this was a red herring; too far-fetched. She couldn't just step into M's job, for one thing, and at some point would have to either fool or involve the father, not to mention E, and others, and, I'm assuming, would have had little time to "learn the ropes."
So (real, original) Mutter is separated (or divorced) and she's lost a son; people have acted unlike themselves, such as by (literally) lashing out at someone, for lesser reasons. She's using an online dating service after having plastic surgery, and critiques her body, apparently contemplating more work. Colored contact lenses are an easy way to make another change in her appearance as part of her fresh start. (E doesn't exactly search every inch of her bathroom looking for them.) Female friends of mine with sons have sometimes complained that they don't share much with them once they reach six or seven. It's not hard for me to believe she wouldn't know Lukas's favorite song - nor guess that it were a lullaby, at his age. I think that Elias would have told her she was wrong regardless of her reply; he'd decided she was an imposter, period.
I think the roaches, skulls, and whatever went on with the (already dead, perhaps, or injured) cat are indicative of E's obsession with death. He puts the cat in a sort of suspended animation, or as close as he can come to it, as he's subconsciously done with Lukas. I believe he imagines the skulls - and the roaches; particularly assuming that's what they are, I don't think they'd be found in such a setting, or that Mutter would tolerate his keeping them. She seems like the type who'd poke and pry around an outdoorsy boy's room to be sure that that house was kept in pristine condition.
As the firefighters attend to the house, oblivious to its presence, Mutter's spirit/ghost, now in the dress we see her wearing in the final shot, walks out toward the field, where she's joined by the spirits of Lukas, and Elias - who ran upstairs as the fire spread, not outside to safety. The three are happily united in death; The End.
Something's up with that food delivery with all the pizzas; I'm not sure what . . . And what the heck were those squishy squarish rock-looking things the "boys" ran across in the beginning of the movie? So cool!!
That's all I've got.

I would postulate a slightly different version to the very meaningful discussion here. It is not their real mother. It is not made clear as to what happened to her but the fact that the lady could not recall the dead son's favourite song lent to the fact that she probably was a friend (or a lover, may be even a twin -they looked similar in the photograph; this could explain the face-lift) to the real mother, who was seen in the photographs, volunteering to tend to the kids in her permanent absence. She would need to pose as the mother in order to not further violate the kid's already troubled psyche. This is why she kept on saying 'that she could not play along'. Being a friend of the mother's she could know some things about the sons but not all, like when Elias claims that his actual mother would never hit him and also would know what Lucas was thinking.
Also Elias asked about the change of her eye colour, this baffled me a bit as to why he was looking for her brown eyes. He just saw the video wherein the lady had brown eyes and came to the mother trying to literally locate the color. But if he knew his mother he would know the actual color of her eyes. This felt a bit strange. I also could not make out the cat's, skulls' and the roaches' references, were they a collective metaphor to Elias' mental state. Suggestions are welcome!!

and whether Lukas died in an accident or Elias killed him doesn't matter: the mother is real.

Wrong. The woman you mention at the end is the spirit of the real mother. There is only one mother here and she's real for the entire movie. She shows obvious signs of traumatic brain injury stemming from an accident of some sort that also took Lukas and provided for the dissolution of her marriage. People recovering from TBI suffer memory problems and often adopt (as with early onset dementia) personalities that are the inverse of their original ones. Hence, the mother's physical altercation with Elias and changed mood that her boy cannot recognize. There is nothing supernatural or mysterious about the mother; Lukas is the only ghost, Elias, the only monster.
It always amazes me how subjective people can be. There are no "interpretations," people, you don't get to just write your own script with paralypsis. Posters here lack basic objectivity.

Nice idea but, no, it's just the director playing with us: the end makes it pretty clear Mom is dead and all we were watching was the perspective of a very disturbed child.
And could they have made the 'twist' any more obvious?

No one talks to the mother ever, except for him,
Sorry but that's wrong. The Mother is seen talking with the priest
after
Elias/Lukas entered the house, so it couldn't have been his/their POV.
The Mother at the end isn't the "real" Mother, it's just some symbolism to show that she has died and has "moved on".
If that was really her, why would she be so calm? And why would the firefighters let her hang around like that, or even the paramedics, without interacting with her?
It's also made obvious that the surgery that the Mother had a surgery that she wanted to have; it was purely cosmetic, and unrelated to any kind of "accident"
So yeah, it was always their real Mother, and she died :/.
And I'm 100% positive that Elias dies as well in the fire, and the final scene is their spirits finally together.
Fine, fine, I'll leave! But first I'm going to bother these peanuts! Hmm? Yes? Hmm? HMM?

Damnit, didn't wanna submit it yet I would've found it better if he actually killed his real mother at the end. But we see (or most people don't) that he didn't, so this makes the most sense to me. Seriously, give it a rewatch and look at that exact shot. Overall, decent movie, I guess.