Learn Hardcore Swedish: De bor på tredje våningen och går upp för trappan varje dag. - They live on the third floor and walk up the stairs every day.

Using i tredje våningen would sound wrong or very foreign; i is for being in an enclosed space (e.g. i huset – in the house), but floors are conceptualized as surfaces you are på (on).

Why is it våningen (with -en) and not just våning?

Våningen is the definite form: våning (a floor) → våningen (the floor).
Here we are talking about a specific floor in a specific building, so Swedish normally uses the definite form:

på tredje våningen – on the third floor (that specific third floor in this building).

Using på tredje våning without -en would sound incomplete or incorrect in this context.

Why is there no separate the before tredje våningen? Why not på den tredje våningen?

Swedish has two options here:

på tredje våningen
på den tredje våningen

Both are grammatically correct and mean the same.
The version in your sentence, på tredje våningen, is a very common, slightly more neutral way to say it. Adding den is often a bit more formal or emphatic, but not a big difference in meaning.

What exactly does bor mean here? How is it different from lever or är?

Bor means live (reside) – where you have your home:

De bor på tredje våningen – They live / reside on the third floor.

Lever means live in the sense to be alive, to live one’s life:

Han lever fortfarande – He is still alive.

You cannot use lever for where someone lives. Är (are) also cannot replace bor here; you’d only use är for temporary location, usually with i/på + place name (e.g. De är i Stockholm – They are in Stockholm).

Why is it går upp för trappan? Could I just say går upp trappan?

The natural idiom in Swedish is gå upp för trappan (also written gå uppför trappan), literally go up along the stairs.
You almost always need för (or uppför as one word) here; går upp trappan is not idiomatic Swedish.
So:

De går upp för trappan varje dag – They go up the stairs every day.

What does the för in upp för trappan actually do?

Here för is part of a kind of prepositional phrase meaning up along / up via something.
Common patterns:

gå upp för trappan – go up the stairs
gå ner för backen – go down the hill

You can also see it fused as one word: uppför / nerför.

Is uppför trappan (one word) different from upp för trappan (two words)?

In modern Swedish, uppför trappan and upp för trappan are both used and mean the same: up the stairs.
Uppför as one word is a bit more traditional/compact, while upp för (two words) looks more transparent to learners, but both are correct and common.

Why is it trappan (the stairs) and not just trappa?

Trappa is a stair / staircase, trappan is the stair / the staircase (definite form).
In Swedish, when you mean the actual stairs in this building, you almost always use the definite:

upp för trappan – up the (building’s) stairs

Using the indefinite upp för en trappa would mean up a (random) stairway, which is less specific and not what you want here.

Can you use tar trappan instead of går upp för trappan to say “take the stairs”?

Yes, you can say:

De tar trappan varje dag – They take the stairs every day.

This is very natural and directly parallels English take the stairs.
Går upp för trappan emphasizes the actual action of going up; tar trappan emphasizes the choice of using the stairs instead of, for example, the elevator.

Can varje dag be placed somewhere else in the sentence? Does the word order change the meaning?

Yes, you can move varje dag:

De bor på tredje våningen och går upp för trappan varje dag.
De bor på tredje våningen och går varje dag upp för trappan.

Both are grammatically correct and mean the same.
The version in your sentence (with varje dag at the end) is the most natural and common in everyday speech.

Why is it tredje? How are ordinals like first, second, third formed in Swedish?

Tredje is the ordinal of tre (three).
The most common ordinals:

första – first
andra – second
tredje – third
fjärde – fourth
femte – fifth, etc.

So tredje våningen is the third floor. The form tredje is irregular; you just need to memorize it, like English third vs three.

What about de vs dom here? I’ve heard people say dom in speech.

In writing, de is the standard subject form, like they:

De bor på tredje våningen…

In everyday speech, almost everyone pronounces de as dom.
So you write de, but you usually say dom in this sentence.