Okay... taking things in order:
"The Noble Eavesdropper":
from his letter to F. Lee Baldwin of 13 Feb., 1934: "I first tried writing at 6, & the earliest story I can remember was written at 7 -- something about a cave of robbers called
The Noble Eavesdropper" (SLIV.380). (He goes on next to say "At 8 I wrote many crude tales (frightfully crude!), two of which --
The Mysterious Ship &
The Secret of the Grave I still have." As "The Secret of the Grave is non-extant and both "The Secret Cave" and "The Mystery of the Grave-Yard" are extant, again, this tends to support the idea that the title above is a mistake for one or both of the others.)
And from his letter to J. Vernon Shea of 19-31 July 1931 (cited in S. T. Joshi's
H. P. Lovecraft: A Life, p. 31): it dealt with "a boy who overheard some horrible conclave of subterranean beings in a cave". There is also this, from his "Some Notes on a Nonentity" (1933):
About this period the weird illustrations of Gustave Doré -- met in editions of Dante, Milton, and the Ancient Mariner -- affected me powerfully.. For the first time I began to attempt writing -- the earliest piece I can recall being a tale of a hideous cave perpetrated at the age of seven and entitled "The Noble Eavesdropper".
-- CE5.208
"The Haunted House":
for the only information we have on that one (at least, that I'm aware of), see my post above.
"The Secret of the Grave":
Ditto, plus the quote given earlier in this post.
"John the Detective":
Ditto, though Joshi speculates that this probably is another of Lovecraft's juvenile "dime-novel" tales featuring King John (for which, see "The Mystery of the Grave-Yard").
"The Picture":
His commonplace book has the following entry: "Revise 1907 tale -- painting of ultimate horror" (
CE5.220). The tale referred to is described in his letter to Robert Bloch of 1 June 1933:
It ["Lucian Grey", an early tale by Bloch] reminds me amazingly of one of the juvenile tales I destroyed -- "The Picture", written in 1907. That is, the theme reminds me. The tale itself is much better than mine. I had a man in a Paris garret paint a mysterious canvas embodying the quintessential essence of all horror. He is found clawed & mangled one morning before his easel. The picture is destroyed, as in a titanic struggle -- but in one corner of the frame a bit of canvas remains.... & on it the coroner finds to his horror the painted counterpart of the sort of claw which evidently killed the artist. The idea was good, but the style was so poor that I don't regret having destroyed it a year after its composition.
-- from Letters to Robert Bloch, p. 15
"The Mystery of Murdon Grange":
from his letter to Rheinhart Kleiner of 27 June, 1918:
My Hesperia will be critical & educational in object, though I am "sugar-coating" the first number by "printing" a conclusion of the serial "The Mystery of Murdon Grange." I will shew it to you when you call. It is outwardly done on the patchwork plan as before -- each chapter bears one of my different aliases -- Ward Phillips -- Ames Dorrance rowley -- L. Theobald, &c. It was a rather good diversion to write it. Really, I think I could have been a passable dime novelist if I had been trained in that noble calling!
-- LRK, p. 145
You will laugh when you see my fictional attempt -- the conclusion of "Murdon Grange". It is a typical dime novel -- with all the time-worn appurtenances of its type!
-- LRK, p. 149
It was that mention of his "aliases", apparently, which long fostered the idea that he had written the whole of the thing; instead, it would seem that the conclusion to the tale was several chapters long, and he used his various pseudonyms for those. Others had a hand in the tale, too, as can be seen from the following:
from his comments (Jan. 1918 DPC) on the amateur journal
Spendrift, for Dec. 1917:
"The Mystery of Murdon Grange" receives its second installment from the not unpracticed hand of Miss Beryl Mappin, and continues in the pleasantly conventional channel mapped out by Mr. Parks in the preceding chapter. The plot thickens!
-- CE1.180
from his comments (March 1918) on
Spendrift for Christmas 1917:
Mr. Benjamin Winskill continues "The Mystery of Murdon Grange" with much cleverness, carrying us back into the past for the source of a strange curse.
-- CE1.188
from his comments (May 1918) on the Jan. 1918
Spendrift:
"The Mystery of Murdon Grange" this month falls into the hands of Editor [Ernest Lionel] McKeag, who furnishes one of the best chapters we have so far perused; possibly the very best. It is exasperating to be cut off abruptly in the midst of the exciting narrative, with the admonition to wait for page 47!
-- CE1.195
"Life and Death":
from an entry dated 1919 in his Commonplace Book:
Death -- its desolation and horror -- bleak spaces -- sea-bottom -- dead cities. But Life -- the greater horror! Vast unheard-of reptiles and leviathans -- hideous beasts of prehistoric jungle -- rank slimy vegetation -- evil instincts of primal man -- Life is more horrible than death.
-- CE5.221
Though George Wetzel claimed to have seen a published version of this story when compiling material on HPL's amateur pubilcations, and to have subsequently lost it, as Joshi notes in
Collected Essays 5, there is some doubt as to whether it was ever actually written, as the entry is not crossed out nor is any other indication made of it having been used. This isn't to disparage Wetzel, but may simply be a case of faulty memory on his part.
There is also one you haven't mentioned: "Gone -- But Whither?" From his letter to Maurice Winter Moe of 6 Apr., 1935:
Whilst rearranging files, I tapp'd a box containing stuff undisturb'd since the Middle 598 [Angell St.] Period -- and found therein the most astonishing array of tail ends of writing materials -- composition books with a few blank pages, incomplete pads, and the like. One composition book of 1905 bears the title of a story about which I had completely forgotten -- Gone -- But Whither? I'll bet it was a hell-raiser! The title expresses the fate of the tale itself.
-- SLV.140
Hope this helps in your quest. Incidentally, if you haven't read Joshi's biography, I highly recommend it. It's one of the most comprehensive pieces on any writer I've seen in quite some time, and supplies an incredible wealth of information on HPL and his work (and world).