can anyone name all the allowed mods for the 1.9-1.12 category

Here is a list for allowed 1.11 mods, if you need different version you can check them here too:
https://redlime.github.io/MCSRMods/?version=1.11

legacy fabric loader for 1.11.2 is allowed by mods?

Yep, it is stated it the rules
"Legacy Fabric Loader is allowed for versions 1.0 through 1.13"

1.11.2 mods

BSRF

maskers

FrustratedF

Minecraft: Java Edition

TKLess_MC

ANJOUU

PAPLERR

Yuuuutoo1207

NZia

1.2.1

1.2.2

1.2.3

1.2.4

1.2.5

1.3.1

1.3.2

1.4.2

1.4.4

1.4.5

1.4.6

1.4.7

1.5.1

1.5.2

1.6.1

1.6.2

1.6.4

1.7.2

1.7.4

1.7.5

1.7.9

1.7.10

1.8.1 Easy

Normal

Hard

Hardcore

1.8.2

1.8.3

1.8.4

1.8.5

1.8.6

1.8.7

1.8.8 4 Players

5-9 Players

10+ Players

1.8.9

1.7.6

1.7.7

1.7.8

1.9.1

1.9.2

1.9.3

1.9.4

1.10

1.11.2

1.11

1.12

1.12.1

1.12.2 2 Players

3 Players

1.7.3 Set Seed

Random Seed

1.0-1.6

1.8-1.11

No F3

1.13

1.13.1

1.13.2

1.10.2

1.14

1.14.2

1.14.3

1.14.4

1.15

1.15.1

1.15.2 Pre 1.8

1.13-1.15

Pre 1.9

1.14+

1.9-1.15

Vanilla

Version

Difficulty

Players

Seed Type (Any% Glitchless)

Version Range (AA)

Seed Type (Any%)

Seed Type

Seed Type (Any% Glitchless Peaceful)

Seed Type (AA)

Version Range (AAdv)

Seed Type (AAdv)

Version Range (Any% Glitchless)

Version Range (Any%)

Version Range (Any% RSG Co-op)

Mods

Version Range (Any% Glitchless (Peaceful))

Version Range (Any% (Peaceful))

Version Range (Any% Glitchless (Demo))

Player Count (AAdv Co-op)

Seed/Glitch (AAdv Co-op)

Version Range (AAdv Co-op)

Seed Type (Combined Any%)

Seed Type (Any% Time Travel)

Seed type (Any% Glitchless Co-op)

Splits (Combined Any%)

If you save & quit/close the game at any point during the run, choose External.

Internal/External (Any%)

Changed version in Ninjabrain-bot resource:

-   [Ninjabrain-bot](https://github.com/Ninjabrain1/Ninjabrain-Bot/releases/tag/1.5.1) [Ninjabrain1] (up to v1.5.1)

Ensure measurements are still accurate after updating, especially with regards to tall resolutions/boat measurements - read the changelog 

Ninjabrain-Bot v1.5.1

Updated Legal Mods

Minecraft

Minecraft Speedrunning Questions Thread

Form for requesting custom map / server leaderboards

SpeedrunIGT

Gamma stuck

IS THIS THE BEST SEED FOR MINECRAFT SPEEDRUNING?

Awesomecuber

AprilSR

skylewl

draconix

nwolc

Luminosity

Droucked

ElRichi

DrGuy

Keima

Winrar

Specnr

AlEmeralds

audioSalix

gaylea

YUMmy_Bacon5

luvvlyjude

taffel

Hayley

tildejustin

drip120

SirJeffersREBEL

the_yuukster

r0hkx

zBlackie_

Haim

Ame_

Leonn

leto_saa

escaperoftheend

Deadpool

Framesarecool

Michal_Alice

Secretivity11