So I drafted up the process message, and Pahein said I could post it, so here it is!
Ok! So we didn't actually solve all of the codes, but we did end up with a dragon we think fits the bill! Everybody involved in the solving of this puzzle is
@
Pahein @
Bailysis @
Dragonwyspr @
Draco981 @
HoneyedBee
Pahein and Bailysis mentioned pretty quickly that it had to be a six letter name since there were six [static]s, and that "we have the same digits" meant Midnight and the other dragon had the same numbers in their IDs, but rearranged.
CODE 1
Bailysis assigned each number a letter here and got
TESTING
as our first message!
CODE 2
Pahein put the second code into a couple different cipher analyzers! The first one indiciated it may be a Wolseley cipher, which needs a keyword. This wasn't helpful. But the second analyzer indicated it was a shift cipher, and gave us
OH NO THIS ONLY WORKS ONE WAY I CANT CHANGE IT BACK TO SOUND AGAIN ALSO I CAN ONLY SEND FIVE MESSAGES AND THEY MUST BE FIVE HUNDRED CHARACTERS EACH SO I HAVE TO BE CAREFUL HOW I USE THEM ANYWAYS MY NAME IS REDACTED AND MY COLORS ARE REDACTED REDACTED REDACTED AND MY GENES ARE REDACTED REDACTED REDACTED AND IM A REDACTED REDACTED AND MY EYES ARE REDACTED REDACTED HOPE THAT HELPS ALSO THESE MESSAGES ARE ENCODED BUT THEY DO TELL ME WHAT THE CODES ARE SO THIS ONE INVOLVES AN ANCIENT ROMAN BUT THEY CHANGE SO THE NEXT ONE WILL USE A STONE KEY AND FIFTEEN FIFTY THREE I SHOULD MAKE USE OF ALL SPACE AS I ONLY HAVE THREE MORE
CODE 3
With that breakthrough, Pahein took note of the "stone key", and put the third code into an analyzer using "stone" as a key. This analyzer indicated it was a viginere cipher, and gave us
WAIT ITS REDACTING ANY INFORMATION I GIVE IT UM LET ME GO GET AROUND THAT SO MY PRIMARY COLOR IS AN ELEMENT MY SECONDARY COLOR IS A CONDITION AND MY TERTIARY IS SOMETHING YOU CAN SEE ALSO MY SEX IS REDACTED AND MY BREED IS REDACTED OH AND I ALMOST FORGOT MY GENES ARE INVOLVING RELIGION GEMS AND AIR HOPE THIS GETS THROUGH AND DOES NOT GET DELETED OH AND MY ELEMENT IS MOVING AND THE TYPE IS REDACTED FYI I HAVE NO IDEA WHY THIS WORKS OR WHY IT BREAKS BUT THE FACT THAT SOMETHING EXISTS AT ALL IS A MIRACLE FOR ME THE NEXT HAS FIVE SECTIONS BRING EACH FROM THE KEY LETTERS DOWN TO A THEN USE RAILS TO GET THE MESSAGE GO FIGURE
CODE 4
Pahein noted the "bring down to A then use rails", and thought it must be a rail fence cipher.
Draco981 saw the mention of religion, gems, and air for the genes, and suspected they may be Cherub / Facet / Smoke. Bailysis expanded upon this and proposed a list of genes it may possibly involve, being
Religion = Cherub, Pharaoh, Starmap
Gems = Alloy, Facet, Malachite, Shimmer
Air = Firebreather, Firefly, Ghost, Smoke, Fans
Bailysis then noted that the tertiary color being "something you can see" would be awful to have to narrow down, since that criterion could apply to most of the FR colors.
I made a list of possible colors for the other two criteria, assuming "element" referred to FR flights, and "condition" referred to words that could be used as descriptors.
Primary (element) = Ice, Shadow, Fire
Secondary (condition) = Antique, Eldritch, Overcast, Royal, Hunter, Radioactive, Rust
Bailysis brought up that an item can be 'diagnosed' as Tarnish(ed) as well, so we added that to the list. They thought Antique was the most likely candidate though.
Pahein had been experimenting with possible solutions to the next cipher all the while. They attempted to rotate the first letter of each section to A and then use the resulting strings in the rail cipher, but this didn't work. Draco981 asked about the key letters. Pahein had assumed they were the first ones for each section. Bailysis wondered if they were the letters from the first code, but Pahein noted that there were only five sections, so that couldn't be right. They opted for attempting the last letters in each section next, which didn't give results either. Their next route was to use the "stone" key introduced in the second code, but then wondered how 1553 was relevant. Draco981 noted that that was the year the modern Vignere cipher was created, and that the first clue's mention of the "roman" referred to the Ceasar cipher.
Bailysis brought up that rail fence ciphers can typically be solved if you know the number of rails (being 5 for this code). Pahein replied that they'd tried that, but each section seemed to be individualy encoded.
They then opted to use an autosolver to get the most likely Caesar rotation for each section, then input those into the rail cipher decoder, which gave us
HMMM WHAT IF I ENCODE IT PAST THE FILTER LET ME TRY SO THE PRIMARY IS ONE SIX ONE TWO ONE TWO ZERO NINE ONE FOUR TWO ONE ONE THREE AND SECONDARW IS BIG Q BIG W FIVE ZERO SMALL A BIG X BIG F ONE BIG Z BIG Q EQUALS EUQALS AND MY TERTIARY IS ONE BILLION NINE HUNDRED FIFTY THREE MILLION SEVEN HUNDRED TWENTY THREE THOUSAND AND SEVEN HUNDRED SIXTEEN HOPE THIS ALL HELPS I GOT TO FIND A BETTER WAY TO GET THIS THROUGH CAUSE I DONT KNOW HOW THIS WORKS BUT MAYBE YOU CAN THE NEXT CIPHER WILL APPARRENTLY MAKE YOU PLAY FAIR AND IT USES THE KEEY AS WELL I DONT KNOW WHAT THAT MEANS BUT AGAIN THATS FOR YOU TO FIGURE OUT ONE MESSAGE REMAINS
CODE 5
Pahein noted that the Secondary code (QW50aXF1ZQ==) decoded to Antique in base64, and the Primary (16121209142113) decoded to Platinum via letternumber code brute forcing.
Bailysis wondered if stone was the key to all of the codes. Pahein shared that they key they used in the rail fence cipher was 18, 19, 14, 13, 4. I noted that the letternumber code for Stone was 19 20 15 14 5, so Pahein's code was one number down on each from that.
Code 4's mention of "playing fair" most likely referred to the PLAYFAIR code, which Pahein noted STONE worked as a partial key for. I wondered if the full PLAYFAIR cipher was STONE [Primary color] [Secondary color] [Tertiary color], as described by Code 4, and came up with STONEPLAIUMQ_____________
We hadn't yet decoded the tert, but Pahein noted that there weren't any colors that could give us enough letters to fill out the rest of the box. They decided to try STONEABCDFGHIJKLMPQRUVWXY, which felt close. They and Bailysis mentioned trying omitting Q instead of Z, and this worked! Following honeyedbee's note that X usually indicates double characters, our decoded message was
IVE FOUND SOMETHING THAT I COULD TRY BUT I HAVE TO DO STUFF SO IT DEFINITELY GETS THROUGH THIS IS MY LAST MESSAGE SO BEST OF LUCK FIGURING THIS MILITARY DIVISION TURNS BACK BUT FINDS THEMSELVES INTERFERING IN ONE OFF PLAN A COSTLY DECISION INTELLIGENCE HAD SET APART A SMALL INSECT FROM ONES EXPERIENCE FOR SOMETIME WILD HORSE COULD BE DEAD ANGEL HAPPENS TO BEAR EVOLUTIONARY BEFORE A MASSAGERE PLACING DECAFFEINATED COFFEE INITIALLY WITH A TEA COULD REVEAL A PARTICULAR FEATURE ON ANOTHER SIDE MILLION DEGREXE TEMPERATURE CHANGE EVENS WITH A TODDS GOVERNMENT ENTERPRISE AND DISAPPEARS
We didn't know what to make of this. I compared it to Pelafina's encoded letters in House of Leaves, which used similar strings of gibberish, but were meant to only have the first letter of each word be significant. Going by this and Pahein's assumption that the code began after "figuring", we got
TMDTBBFTIIOOPACDIHSAASIFREFSWHCBDAHTBEBAMPDCIWATCRAPFOASMDTCEWATGEAD
Obviously this was still encoded. I tried throwing this into a code analyzer, which brought up the Bazeries cipher as a possibility. This one required a lot of keys though, and we didn't know where to go from there.
Here, Pahein input everything we'd previously determined into the dragon search to check our options, and we got 17 results, and 3 with 6-letter names. Pahein realized that one of those,
Keiden, had an ID# that was an anagram of Midnight's.
Keiden's genes/colors were Platinum Cherub / Antique Facet / Dust Smoke, and she had Water eyes. This followed all of the previously established clues, noting that Platinum is an element on the periodic table, and Water worked as something that moved.
We never solved that fifth code, but we're pretty confident we found the
answer!
Trust, there'll be more soon 
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