This quest is very long. In the YouTube video below I had to cut out about 20 minutes to keep within my time limit of 20 minutes. If you are going to do this quests be sure to allow around 30 minutes to an hour depending on how fast you usually go through dungeons. I had the game bug out at the end as well.
Anyway, if you are just looking to enter this dungeon without starting this quest first you can find it here:
Main Body of Mzulft
Mzulft isn’t a particularly hard dungeon. You will mainly meet Falmer who are tough. I found the best way to deal with them is to sneak up on them with a bow and arrow and kill as many of them as possible until they detect you. When you are selecting targets with the bow and arrow try to go for enemy mages first but also archers because they will be able to do damage to you regardless of your position. Then I just take care of the rest the normal way. I found that if large groups of them were left retreating into a tight passage is good because they will only be able to attack you one at a time. They are no match for you one on one.
Eventually you will run into a Falmer Shadowmaster in a large hall in the dwarven city. Be sure to take out the archers and soldiers around him first, sneaking is particularly useful here because you can switch sides as there are two main entrances to this hall. After you have killed the Shadowmaster be sure to loot the focusing crystal from him, it is essential later and if you don’t take it now you will be rewarded with having to go back later.
Dwarven Centurion Master
I didn’t run into the locked door, but if you are trying to get to the quest marker as fast as possible and not exploring everything like me you would have run into a door that you can’t pick. Simple go through the door on the opposite side of the hall and follow the corridor there until you meet the Centurion Master. He is stuck in his little room so you can pick him off with bow and arrow or magic without him ever being able to do anything. I ran in there, did some damage to him with my sword and ran out when I was low on health to heal. After you have killed him, by the way enchantments and poisons do not work on dwarven stuff, there is a chest in that room with a key for the locked door.
Solving the Focusing Puzzle
I initially killed Paratus Decimius because in video games I don’t like to be told what I have to do. However, if you kill him you can’t finish this quest.
To get the beams in the right place blast the focusing crystal three times with cold. In case you go too far use fire to correct your mistake. If you don’t know the requires spells there are spell tone books behind the console on a stone bench. After the beams are in the right place use the buttons on the console to move the rings so that the spherical objects on the rings have the light beams pointing at them. You will need to follow Paratus to complete this puzzle.
After you have completed your objectives in Mzulft the quest marker will direct you back the way you came in. However, there is a much quicker way. In the corridor where you met Paratus there is another hall way that has a door at the end. It is locked but you should have the key by now. This door will lead straight to Skyrim.
Breaking the Spell at Winterhold
Just use any kind of destruction magic to break the spell stopping you to go into the Hall of the Elements.