Instead of charging ahead, either use a catious sniper tactic to slay the Falmer guard and its friend from the stairs who comes up to check on it, or use a quick brutal charge to mow it down and then crush the ally that comes to avenge it. Either way, once that is done you should gather the two pieces of Dwemer scrap from where they sit beside the giant metal vase near where you entered the room.
Move on to reach a spot where the hall is obscured by crumbled rubble. To the left of you is a clear path, which leads right to the back of a Falmer Gloomlurker, who you can easily take out without drawing undue attention. From here, though, you have two options- the next area is all connected and full of a dangerously large group of seven Falmer, roughly half of them Shadowmasters and Gloomlurkers, with varying degrees of magical and martial skill and a single pet frostbite spider. You can attempt to enter the area with them and murder them all, but this is a very good way to get dogpiled, and if you’re not prepared to fight a lot of enemies simultaneously you will die very, very quickly. Doughty warriors and offensively powerful spellswords can get away with this, as can alchemists with a few spare gallons of healing solution.
Alternately, you can creep up to the rubble and fire an arrow or spell at one of the patrolling Falmer through the small hole that you can see through, but not climb through. While this does still draw all seven of the enemy to your location, you can sit and wait for them, which lets you snipe them, ambush them from behind a corner, and generally face them in a strung out group rather than in a frantic, confusing mass of black weapons and armor and pale skin.
Either way, you’ll need to figure out how to manage this fight to continue. Once the Falmer are all dead, and their little spider too, loot the corpses and step into the area where the lone Falmer Gloomlurker was standing and waiting. Before you descend the steps, check to your right for a locked Dwemer gate, behind which are several pieces of smeltable scrap, an apothecary satchel, a valuable potion, and a small stone chest full of loot.
The stairs down from here lead to a hallway with several pieces of Dwemer scrap in it, which then connects through a stone doorway to another hall with Dwemer scrap in it. This leads to a room with several pieces of Dwemer scrap, which has stairs leading up to a platform with- you guessed it- more Dwemer scrap. From here you can head up a stairway to reach the area you could see through the collapsed hall, and turning left will bring you to one last hallway (this one oddly lacking in Dwemer scrap) that leads to a large door and has an offshoot to the left.