Learn Hardcore Icelandic: Húsnæðið í miðbænum er dýrt, en það er nálægt vinnunni hennar. - The housing downtown is expensive, but it is close to her work.

húsnæði = housing, accommodation (not a specific unit; more abstract or collective)
hús = house / building (a concrete building)
íbúð = apartment / flat

The form húsnæðið has the definite article attached:

húsnæði = housing
húsnæðið = the housing / the accommodation

So the sentence is talking about the housing (or the accommodation) in the city centre, not just any housing in general.

Why is it í miðbænum and not í miðbæ? What is going on with this -num ending?

Miðbær means city centre / downtown.

miðbær = city centre (indefinite, nominative)
miðbærinn = the city centre (definite, nominative)
í miðbæ = in a city centre / in city centres (indefinite, dative)
í miðbænum = in the city centre (definite, dative)

Two things are happening in í miðbænum:

The preposition í
- With location (where something is), í takes the dative case.
- So miðbær → dative: miðbæ.
Definiteness is shown with a suffix
Icelandic usually attaches the definite article to the end of the noun:
- bær → bærinn (the town)
- miðbær → dative definite: miðbænum (in the city centre)

So í miðbænum literally means in the city-centre-the, i.e. in the city centre.

Why is it er dýrt and not er dýr?

The adjective dýr (expensive) has to agree with the gender, number and case of the noun it describes.

húsnæði is neuter singular.
The neuter singular predicate form of dýr is dýrt.

So:

Húsnæðið er dýrt. = The housing is expensive.
Bíllinn er dýr. (masc.) = The car is expensive.
Íbúðin er dýr. (fem.) = The apartment is expensive.

dýr is the masculine/feminine form; dýrt is the neuter form. Because húsnæði is neuter, the sentence must use dýrt.

What does en mean here, and is the comma before it required?

en is a coordinating conjunction meaning but / however.

Húsnæðið í miðbænum er dýrt, en það er nálægt vinnunni hennar.
= The housing in the city centre is expensive, but it is close to her work.

The comma before en is normal and standard in Icelandic whenever you join two independent clauses:

… er dýrt, en það er … = … is expensive, but it is …

So yes, this comma is expected in correct written Icelandic.

What does það refer to? Is it just a dummy subject like English it?

In this sentence, það is a real pronoun referring back to húsnæðið.

Húsnæðið í miðbænum er dýrt, en það er nálægt vinnunni hennar.
→ það = the housing / that accommodation

Icelandic also uses það as a dummy subject (like it is raining → það rignir), but here it is not dummy; it is a normal third-person singular neuter pronoun, agreeing with húsnæði, which is a neuter noun.

Also, Icelandic normally does not drop subject pronouns in this kind of sentence, so you need to keep það.

What does nálægt mean, and why is vinnunni in that form?

nálægt is a preposition meaning near / close to.

It always takes the dative case:

nálægt húsinu (near the house – dative)
nálægt stöðinni (near the station – dative)
nálægt vinnunni (near the work / workplace – dative)

vinna (work) is a feminine noun:

Nom.: vinna (work)
Acc.: vinnu
Dat. indefinite: vinnu
Dat. definite: vinnunni (the work / her job / her workplace)

Because nálægt requires dative and we want the work / her job, we get vinnunni.

In context, nálægt vinnunni hennar usually means close to her workplace / job, not physically close to the abstract concept of “work”.

Why is it vinnunni hennar and not something like hennar vinna?

Icelandic normally puts the possessive pronoun after the noun, not before it:

húsið mitt = my house
bíllinn hans = his car
vinna hennar is grammatically possible, but in practice the definite noun + possessive after is far more natural in this context:
- vinnan hennar / vinnunni hennar = her job / her work / her workplace

Here we need dative case because of nálægt, so:

Nominative: vinnan hennar
Dative: vinnunni hennar

So nálægt vinnunni hennar = near her work / workplace, and this order (noun + article + hennar) is the normal, idiomatic pattern.

What is the difference between hennar and sín/sinni/sitt? Could we say nálægt vinnunni sinni here?

hennar is the ordinary third-person feminine possessive pronoun: her. It can refer to any woman previously mentioned in the context.

sinn / sín / sitt is the reflexive possessive: her own / his own / their own, and it refers back to the grammatical subject of the same clause.

In this sentence, the subject is húsnæðið (the housing), not a person:

Húsnæðið í miðbænum er dýrt, en það er nálægt vinnunni hennar.

So vinnunni hennar refers to some woman’s work (the woman mentioned in the context), and that does not have to be the subject, because the subject is not human anyway.

You cannot say nálægt vinnunni sinni here to mean her own work because sinni would have to refer back to the subject húsnæðið, which doesn’t make sense.

If the subject were she, then sinni would be correct:

Hún býr í miðbænum. Húsnæðið er dýrt, en það er nálægt vinnunni sinni.
= She lives in the city centre. The housing is expensive, but it is close to her own work (her workplace).

Here sinni refers back to hún, the subject.

Could you remove í miðbænum or vinnunni hennar and still have a correct sentence?

Yes, grammatically you can remove those phrases; they are just providing more detail. For example:

Húsnæðið er dýrt.
= The housing is expensive.
Húsnæðið í miðbænum er dýrt.
= The housing in the city centre is expensive.
Húsnæðið er dýrt, en það er nálægt vinnunni hennar.
= The housing is expensive, but it is close to her work.

All of these are well-formed sentences; you just lose some information when you delete the phrases.

Is the word order fixed, or could you say something like Húsnæðið í miðbænum er dýrt, en nálægt vinnunni hennar er það?

Icelandic word order is relatively flexible, but there are natural and unnatural options.

Húsnæðið í miðbænum er dýrt, en það er nálægt vinnunni hennar.
→ Completely normal and natural.
Húsnæðið í miðbænum er dýrt, en nálægt vinnunni hennar er það.
→ Grammatically possible, but sounds marked / poetic / emphatic. It puts extra focus on nálægt vinnunni hennar (“but close to her work it is”).

For everyday speech and writing, you should stick with the neutral order used in the original sentence.