Finally had a chance to look at this. Here are my notes:

First, your file is dependent on TR_Mainland.ESM. This is probably just because we gave you confusing instructions, but this shouldn't be the case. When working on a quest claim, or with a section file that contains dialogue, you should always load TR_Mainland.ESP alongside it. This is because Morrowind has a bit of a fucky way of storing the order of dialogue entries. Every dialogue entry also lists the IDs of the preceding and subsequent entry. If you add dialogue to an .esp in between existing lines (which is basically any time you add dialogue), and then load the file without the files containing any preceding or subsequent dialogue IDs, shit will get fucky and your dialogue will forget which lines it's supposed to follow.

Having said that, it was easy enough to remove the dependency in Wrye Mash, and everything still seemed to work just fine. File without dependency in the attachment.

So, to the quest itself. I thought it was a very enjoyable addition to the interior, and one that really helped bring out its unique character. Good job! I do have a few nitpicks, though. The technical aspects:

• The IDs need to be fixed - you've already committed to doing that, which is good, but it needs to be mentioned here.
• T_bk_Vandirelyon_Taldam_Book_01 appears far too often in this interior, it's literally everywhere. If you remove half of them, it'll still have plenty.
• T_bk_Vandirelyon_Taldam_Book_01 appears unfinished, and its use of Capitalization for emphasis (while allowed) seems rather inconsistent. This book would do well to be expanded and fixed up a little.
• T_Bk_Vandirelyon could use a Capitalization pass to be more in line with the other book.
  • These should probably have been caught during the int review, but I'm noting them here regardless. These IDs also need to be updated - T_bk_Vandirelyon_Taldam_Book_01 could possibly stay, if it gets a proper literature review and we move it to Tamriel_Data, but T_Bk_Vandirelyon is far too specific to this int, and should just be a unique int-specific note, so TR_m7_Vandirelyon_note, or something similar, would do.
• T_bk_Vandirelyon_Sacr_01 contains some spelling mistakes.
  • Sacriment --> Sacrament,  
  • shall take offering to Taldam --> shall take the offerings to Taldam,  
  • unlocking it's hidden chamber --> unlocking its hidden chamber
  • Book could use a quick language pass, too, it reads a little too much like an instruction manual rather than a sacrament.
• T_chest_small_Vandir_01  - I appreciate the little script on this container, but there is no reason for this not to open before the quest has been started. If this were me, I'd just throw a fire trap on this chest and remove the script.
• T_Vandirelyon_Button is very difficult to spot - and I like it. 
• T_Vandirelyon_Wall_01 currently moves to the right, and once it does, it clips right through the wall into the little alcoves with the crates in the surrounding hallway. Now, I'm pretty sure most people won't notice this, but I did, and I think you should just make the wall move to the left instead of to the right, so that it moves into the empty area and doesn't interfere with anything else.
• Speaking of moving objects, here's a little MWScript fuckery for you: if you just move an object, it'll often reset its position when you save and reload. This means saving and loading might interfere with the sequence you're setting up here. Instead of using Move, you could simply SetPos the thing (I'd honestly not bother moving the button, just focus on the wall) to a variable you change with GetSecondsPassed every frame. Alternatively you can, each frame, call a script like this, that will actually *set* the position to its actual position after it's been moved.

float posY
Move Y -10
set posY to GetPos Y
SetPos Y posY

• Having said that, you did a good job explicitly calling SetPos after the timer is done - that at least ensures that everything moves back into its proper place afterwards, and that any issues caused during one cycle won't affect the next!
• I like the mechanism where the player has to equip the robe in order to pass the door. However, right now it is a little anticlimactic, and the door just looks like any other door but with a messagebox attached to it. If I were you, I'd fancy up this door with some decoration, some custom arrangement of bones and skulls and stones and flames, what have you. Make it fancy. Make it stand out. Make it look important. Throw in a few of those velothi prayer stools, maybe. That way, getting a messagebox isn't such a surprise, and preserves the player's immersion a little better.
• It's rather difficult to navigate Vandirelyon, Sewer. This confuses the AI on your flame atronach and can make the fight a lot easier than intended. It might be a good idea to smooth out this place a little, or at the very least remove the one lava pillar thing in the guy's alcove and create a bit more of a useable walkway.
• The journal TR_VandirelyonQuest (again, needs a new ID, TR_m7_BeneathVandirelyon or something):
  • Spelling: ceramonial -> ceremonial, Taldom->Taldam
  • The player doesn't know (for certain) that what's being worshiped is a Flame Atronach. The journal needs to reflect this uncertainty. In fact, most of your journal entries contain a little too much handholding. Remember that there's a way to view all the journal entries for a specific quests, since Tribunal if I'm not mistaken, so you don't have to repeat all the information or tell the player the next step all the time. I'd do this:
    • 10: "I have found a document within Vandirelyon. It appears that the cultists within the stronghold worship a creature that dwells beneath the keep. The scroll suggests that one may only reach this creature by accessing the sealed door while wearing a ceremonial Searing Robe. The robe is said to be hidden in a secret compartment which can only be opened with a Burning Signet."
    • 20 (new): "I have found a sealed door within Vandirelyon. Perhaps this is the door mentioned in the scroll."
    • 30: "I have found a small chest containing a Burning Signet ring."
    • 60: "I have found the Searing Robe in a secret compartment."
    • 80: "Wearing the Searing Robe allowed me to pass the sealed door in Vandirelyon."
    • 100: "I have Destroyed Taldam Ignatus, a powerful Flame Atronach, beneath Vandirelyon."
• The rewards: a little disappointing. If I were you, I'd make both the Burning Signet and the Searing Robe a little more interesting, as currently there's no reason to ever use these beyond this quest. How about adding a strong Fire Shield enchantment to the Searing Robe on top of the Fire Damage, and turning the Burning Signet into a ring that does low-maginute Weakness to Fire & Fire Damage to the player, and high-magnitude Weakness to Fire & Fire Damage on target? That way, if the player has enough fire resistance, they might actually be able to make use of these items.
  • Another random thought, I think the Boots of the Atronach unique item are already planned to be elsewhere, but *perhaps*, if you ask Cicero nicely, your big bad Atronach could drop an item that could be used to empower these boots - turn them into proper burning Atronach boots that leave a trail of fire behind the player as they walk, for instance. That's something for the future, probably, but it'd be hella cool.

And, my personal experience and recommendations:

For a first quest, this is a great start. It's quite competently made, and I noticed no errors in the scripts, beyond the (rather advanced and finicky) Move stuff, and that's a pitfall I manage to stumble into frequently as well. However, it is important to consider how a quest plays, as well. Currently, I'm missing the human element. Perhaps this is because the fortress hasn't been NPCed yet, but still, I would love to have somebody to talk to and figure out what the hell is actually going on in this interior. I'd suggest placing one non-hostile NPC in this int, who can ask you to kill the Atronach and give some scant exposition on what's downstairs. Perhaps there is a remorseful cultists or a desperate slave in the lovely little prison cell in the Lower Keep - who can serve as an alternative way to start the quest. I wouldn't have too much dialogue on this NPC (so a slave might be best) but they could tell you that something evil lives downstairs and that these cultists worship it, and that there's a scroll in Underground that might have more information. So, in short:

• Add an NPC to the little cell in Lower Keep who serves as an alternative way to start the quest - and lets you show us your dialogue skill.

All in all though, good work, I'm looking forward to seeing the final result and it fits the interior very well - it'll be a great addition to the TV release!

Edit: Also, if you feel up to it, I definitely would not object to you NPCing this interior while you're at it. But that's not required for me to promote you - just fix the things listed above first.