The Jade Rabbit hopped up to Chang'e with a plain white box. "I've got a present for you!"

"Another elixir of life?" the immortal moon goddess sighed. "I've lived through so much. The horrors of past centuries, I want to get them out of my head but can't!" Reluctantly she took the box.

"That's why I got this for you; it should help you calm down. It is not an elixir. Its identity is given by the puzzle I scribbled on the side – don't open it until you solve it!"

This was what Chang'e saw:

First letters downstairs @ last letters downstairs, then go upstairs

1 2 3 4
predator of Australia (5)
inflammation of skin (6) mother of presidents (8)
quote of raven (9) country of Troubles (7) property of one (7)
birthstone of December (9) institute of learning (10) messenger of God (5) building of bees (9)

She spent a whole moon trying to figure this out, but couldn't. Eventually, out of sight of the Jade Rabbit so as not to anger it, she tore the box open.

What did she find inside?

The Jade Rabbit was too hasty to write this on the other side of the box:

            .
.@
. +@+ .  =  ...
..    ..    ....
...   ...   .....
....  ....  ......

• Lol Chang'e probably only speaks ancient Chinese. Jun 3, 2021 at 2:07

MikeQ is almost there! (And I think it's too bad that he's lost interest; for my money, adding an extra hint and then tweaking it really doesn't make this a "chameleon question".)

Start with the words Vicky and Mike found. Take their first letters, starting at top left and reading down by columns, then an "@", then their last letters, reading the same way. (Apparently this is the meaning of "downstairs".) Then take that sequence of 21 symbols and write it into a side-6 triangle, starting at the bottom right and reading up by columns. ("Upstairs".) We get:

A
D @
Y O U
C A N T
L E A V E
B E H I N D

And now, as Mohirl pointed out in comments and Parcly clarified further,

that initial "A" should be interpreted as a ∀ for-all symbol, and "D@" as "dat" = "that". The Jade Rabbit has given Chang'e an album by the band U2.

Credit where due:

I had rejected the idea of that album being relevant because I didn't see how "A D @" was close enough to "all that". Mohirl spotted D@ = that. Parcly Taxel explained A = ∀ (which I really ought to have thought of, being a mathematician myself). And of course the actual word-finding was done by Vicky and Mike.

• Maybe Chang'e is supposed to relax by rot13(yvfgravat gb gur nyohz "Nyy gung lbh pna'g yrnir oruvaq", jvgu "gung" ercerfragrq ol q@. Zvffvat gjb yrggref bs "Nyy" gubhtu.) Jun 3, 2021 at 9:35
• @Mohirl rot13(Ghearq N zrnaf sbe nyy. Punat'r nf gur erpvcvrag vf npghnyyl whfg n punenpgre gung svgf gur zlgubybtl, ohg gur Wnqr Enoovg'f cvalva qbrf unir n yvax gb gur chmmyr nafjre.) Jun 3, 2021 at 9:57
• Ah -- I found that album but never thought of rot13(A for "for all") or rot13(D@ for "that") and therefore thought the similarity was coincidence. D'oh! Jun 3, 2021 at 10:44

Partial answer (credit goes to Vicky's original answer for some of these):

dingo
eczema | virginia
nevermore | ireland | numeric
turquoise | university | angel | honeycomb

Now for the guessing.

There are 10 words in the matrix. The clues suggest that the cipher involves arranging 10 letters (first letters downward), then @, then another 10 letters (last letters downward). Then this needs to be rearranged "upstairs" somehow.

Maybe the "downstairs" clue means to take the first letters of each diagonal, starting from the outermost diagonal (dingo, virginia, numeric, honeycomb) and progressing downward. Then repeat for the last letters of each word in that same order: DVNHEIANUT@OACBADLEYE

Or maybe "downstairs" means taking the first letters of each word in each column, downward, then left to right by column. Then repeat for the last letters of each word in that same order: DENTVIUNAH@OAEEADYCLB

Edit: This puzzle's content has changed several times, so this is where I stop working on it.

As a final note, the question is currently tagged "cipher". Nothing seems to indicate a rotation or keyed cipher, so I suspect a translation cipher (same letters, different order) is involved. Perhaps it is an anagram of the letter sequences above. Considering the story and figures (Jade Rabbit and Chang'e) in the first part of the puzzle, it may be interesting that

anagrams of AAABCDDEEEHILNNOTUVY (the 20 letters above, alphabetized) partially include: ACHE, ADVICE, BUNNY, CHEAT, DEATH, DECEIT, DEITY, HEAD, HEAVEN, HEAVENLY, HOLY, IDEA, IDEAL, TEACH

But I don't know if this is part of the intended solution.

• @ParclyTaxel That information changes the puzzle... How about now? Jun 2, 2021 at 22:25