Not being a Dungeons & Dragons player myself, this was very hard to work through - but I've got there in the end...
Astrid's message is shocking (I assume...!):
I AM TASHA'S DAUGHTER. In other words, she isn't who you think she is but actually the daughter of Tasha, the archmage in the title of the sourcebook for the 5th edition of D&D, Tasha's Cauldron of Everything. This is not good news.
How to extract this message? There are several steps, heavily reliant on D&D knowledge...
Step 1:
The first line of Astrid's message is written in the 'lokharic' script of D&D's Draconic language:
The message translates as 'LDIUBZJ'.
Step 2:
The equation $y = 11x + 3$, coupled with Hint 2's suggestion of 'a fine cipher' is the key needed to decode this ciphertext, which is written in an affine cipher. Following the decoding procedure yields the word 'WARLOCK'.
Step 3:
Coupled with Hint 3's 'damage' and Hint 4's 'spell', this suggests that what follows beneath is some representation or other of various damage-causing spells used by warlocks in the game.
The symbol represents the type of damage done and took a bit of trial and error before I'd worked out which of the 13 common damage types were being represented here. Ultimately, they work out as:
- eye = psychic;
- skull = necrotic;
- soundwave = thunder;
- sword = slashing;
- star = force;
- flame = fire;
- lightning bolt = lightning (that was the easy one!).
Moreover, the polygons beside them have two functions:
1. Their shape represents the shape of the faces of a particular die used when casting the spell:
- triangle = d8 (i.e. an 8-sided die - other dice use similar notation);
- square = d6;
- 'teardrop' = d4 or d10;
- pentagon = d12.
2. The number shown indicates the quantity of these dice that are used when casting the spell.
This means we can resolve the list as follows...
...helping us identify exactly which spell is being referred to in each case. (After many false starts - as I had to search the web for these - I found this site the most useful by far. Sadly I came to it very late in my search!)
[9] eye, square x4 = psychic 4d6 = FEEBLEMIND
[9] skull, triangle x7 plus XXX = necrotic 7d8+30 = FINGER OF DEATH
[1] eye, square x4 = psychic 4d6 = FEEBLEMIND (again)
[6] soundwave, triangle x3 = thunder 3d8 = SHATTER
[5] sword, triangle* x4 = SLASHING 4d4* = CLOUD OF DAGGERS
[6] skull, triangle x8 = necrotic 8d8 = BLIGHT
[4] skull, square x8 = necrotic 8d6 = CIRCLE OF DEATH
[3] star, teardrop x1 = force 1d10 = ELDRITCH BLAST
[5] wave, triangle x3 = thunder 3d8 = SHATTER (again)
[12] fire, teardrop x2 = fire 2d10 = HELLISH REBUKE
[9] skull, square x8 = necrotic 8d6 = CIRCLE OF DEATH (again)
[4] skull, square x3 = necrotic 3d6 = VAMPIRIC TOUCH
[13] sword, triangle* x4 = slashing 4d4*= CLOUD OF DAGGERS (again)
[1] skull, triangle x1 = necrotic 1d8 = CHILL TOUCH
[10] skull, triangle x7 plus XXX = necrotic 7d8+30 = FINGER OF DEATH
[1] skull, square x3 = necrotic 3d6 = VAMPIRIC TOUCH (again)
[2] lightning bolt, pentagon x1 = lightning 1d12 = WITCH BOLT
* Note that in 2 cases, the OP has supplied an erratum, stating that the triangles should actually be squares. However, I believe they should actually be 'teardrop' shapes to suggests d4 dice (not d6), in order for the puzzle to unfold correctly...
Step 4:
The only part unused thus far is the Roman numeral at the start of each line. In the step above I have already decoded this to regular numbers, and these now need to be used...
...to index into the name of each spell, selecting the letter in that position:
[9] FEEBLEMI[N]D = N
[9] FINGER OF [D]EATH = D
[1] [F]EEBLEMIND = F
[6] SHATT[E]R = E
[5] CLOU[D] OF DAGGERS = D
[6] BLIGH[T] = T
[4] CIR[C]LE OF DEATH = C
[3] EL[D]RITCH BLAST = D
[5] SHAT[T]ER = T
[12] HELLISH REBU[K]E = K
[9] CIRCLE OF [D]EATH = D
[4] VAM[P]IRIC TOUCH = P
[13] CLOUD OF DAGGE[R]S = R
[1] [C]HILL TOUCH = C
[10] FINGER OF D[E]ATH = E
[1] [V]AMPIRIC TOUCH = V
[2] W[I]TCH BOLT = I
Altogether, this yields the string NDFEDTCDTKDPRCEVI.
Step 5:
Finally...
...we need to decode this string using the same affine cipher as before. This process gives us the final string IAMTASHASDAUGHTER, which can be respaced meaningfully as I AM TASHA'S DAUGHTER.
PS How did I solve this as a D&D newb? With great difficulty! Some key steps:
1. I identified the cipher by searching for 'DnD dragon language' in a web browser, using Hint 1, and got a hit.
2. Searching for 'fine cipher' led to the discovery of 'affine ciphers'.
3. Interpreting the list was a complete headache for me, and I went down several dead ends (over several weeks since I first got this far!), trying to match polygons, quantities, symbols and the Roman numerals to various aspects of a game I had never played. However, eventually it hit me that the polygons matched up to faces of common dice used in the game. Then by researching 'DnD warlock spells' I learned that spells dealt different types of damage, which were likely represented by the symbols. I was unaware of whether there is a standard symbol key for these, so I had to make some deductions (fire and lightning came easily, the skull being 'necrotic' followed - reasoning that there weren't enough 'poison' type moves - and the eye as 'psychic'. I was unable to differentiate the sword as being either 'piercing' or 'slashing' and was unsure on the soundwave and star so left them for later...).
I got stuck at this point for ages and only came back to the puzzle today, realising almost straightaway that the number of polygons might represent the number of dice used in the spell. Thus began many searches of the kind 'DnD spell necrotic 8d8', trying to identify the spells in question (until I found the website mentioned above - then it became a series of Ctrl+F usages).
4. I had reasoned that the Roman numerals would likely represent indices, helping us extract relevant letters, but performing this on the spells I had chosen just yielded nonsense. After a while I had a brainwave that perhaps the affine cipher needed to come into play again, and my first attempt at letter extraction yielded a string that ended in DAUZHTER. Reasoning this to be a close match to 'DAUGHTER', I attempted to rejig my list and find other suitable spells until the whole thing spelled out a phrase. It took a while, but I got there in the end!
