J.R.R. Tolkien wrote the stories of the Middle-Earth and he has passed away, so can any new information be added to these stories without his approval?
No, no new information could be added.
But "canon" in Tolkien is a very difficult matter. He was working on some of the stories for nearly 50 years on and off, and his conception of many elements changed significantly over this period. His son Christopher traces the development and evolution of some of the elements in his massive 12-volume History of Middle-Earth series, but even he doesn't always know exactly how it worked, and several times in a later volume notes that he has discovered something that contradicts what he set out in an earlier one. Often his father wrote contradicting texts at different times on the same piece of paper, sometimes overwriting in pen something completely different he had originally written years earlier in pencil.
This is most evident in the published Silmarillion. This was Christopher's best effort at the time, only a few years after his father's death, to put together a coherent statement of the mythology for publication. As he notes in the introduction to that book, the various elements of the mythology were in quite different states: some of them fully-fleshed out narration, others just outlines. He worked with the fantasy author Guy Gavriel Kay to expand some of the more basic ones and finish others.
But just because that book was published as a single finished item doesn't necessarily make it "canon", and Christopher later came to regard his decision to publish in that form as a mistake. Hence the publication of Unfinished Tales and then the HoME series, where he attempts to follow the creative process itself and show extracts from the different and contradicting stages, rather than attempting a "best guess" as he did with the published Silmarillion.
The Tolkien Estate explicitly addresses this on their website about the Children of Hurin:
The author wished for his third son, Christopher Tolkien, to become his literary executor after his death, and Christopher's first task was to organize the huge volume of papers that JRR Tolkien had created during his lifetime ; the first published work on the subject to appear was The Silmarillion in 1977.
Given Tolkien gave his approval for Christopher to act in this capacity, any further publications are generally regarded as canon - not only because of the aforementioned approval, but also because Christopher's "work" is largely Tolkien's own words where Christopher has "filled in the gaps" due to the source documents not fitting together perfectly:
[The Children of Hurin] existed in many unfinished and heavily reworked forms. As a culmination of thirty years' work on his father's papers, and having already published such fragmentary and condensed forms of the tale of Túrin as part of the development of « The History of Middle-earth », Christopher Tolkien has now succeeded in assembling the multiple variants, unfinished pieces, and outlines of the tale to produce a standalone and complete version, entirely in the author's original words.
The Silmarillion was similar, except it contained original work by Christopher and Guy Gavriel Kay to fill in said gaps, as opposed to it being done "entirely in the author's original words".
Christopher Tolkien actually published several books after J.R.R. Tolkien's death - The Silmarillion, Unfinished Tales, the History of Middle-Earth series, and The Children of Hurin. No one else has written an "official" book set in the Lord of the Rings universe, and presumably they would have to obtain permission from the Tolkien estate to do so.
Christopher Tolkien, while his edits did shape the books that he published, did not add major portions to those books and he has not written any complete works set in that universe himself. As far as I can find, J.R.R. Tolkien did not leave provisions for additions to the Lotr "Canon", and since none have been written, it's safe to assume there are no provisions for additions.
JRR Tolkien passed away, but several books have been published on his name after his death (all material writted by JRR Tolkien, but edited and/or published by his son Christopher).
JRR Tolkien wrote a lot of unpublished stories and background material over many years (sometimes contradictory or difficult to decipher), so theoretically more material could be published on his name that hasn't been published before and it would arguably become "canon" even if JRR Tolkien already passed away.
If Silmarillion or Unfinished Tales or the Children of Hurin (etc.) are canon for you, then this new material (assuming it will be published, of course) will be canon as well.
This situation happened a lot in history with plenty of authors and a lot of posthumous or unfinished books are actually credited as "true" work and creation of the author (canon).
I think the idea of 'canon' for Middle Earth is a tricky concept, in that Tolkien viewed his writings as an ancient mythology for England, and as a scholar of existing mythology (Beowulf etc) he knew exactly what form this took. That there are several and varied accounts of different events in the mythology is not evidence of a stream of canon and other non-canonical narratives. LotR is of course pretty much bedded down, to a very slightly lesser extent The Hobbit (recall the 'updating' of Bilbo's ring story. Is the first edition of The Hobbit canonical though and through?).
Unless Tolkien explicitly stated that he wanted, as they say, a single source of truth, then I would take the total collection of his Middle Earth writings as 'canonical', and analyse them from the point of view of recovered historical documents, rather than trying to extract a single narrative and make that the single true version.
Yes and no.
An extract from JRRT's will is published online at John Rateliff's Blog and this extract explicitly states that Christopher Tolkien has the rights to:
publish edit alter rewrite or complete any work of mine
which may be unpublished at my death or to destroy the whole
or any part or parts of any such unpublished works as he
in his absolute discretion may think fit and subject thereto.
In other words Christopher Tolkien (and only Christopher Tolkien) may add new information of his own invention to unpublished works and this would be canon in accordance with JRR Tolkien's explicit intent.
However, the question of "approval" still stands. JRRT did of course approve of CT doing this (in his will), but he doesn't have to (and is obviously not in a position to be able to) approve of specific items of information.