Learn Hardcore German: Zum Glück haben wir den Unfall gut überstanden. - Fortunately we got through the accident well.

Zum Glück literally means “to the luck” (from zu dem Glück), but idiomatically it means “luckily / fortunately.”
It’s a very common sentence adverb used at the beginning or in the middle of a sentence to comment on the whole situation: Zum Glück haben wir den Unfall gut überstanden. / Wir haben den Unfall zum Glück gut überstanden.

Why is it Zum Glück and not Zu Glück?

Zum is the contraction of zu dem.
The noun Glück here is used with a definite article (das Glück → dem Glück in dative), so zu dem Glück becomes zum Glück.
Fixed expressions like this almost always use the contracted form: zum Glück, zum Beispiel, zum Essen, etc.

Why is haben used as the auxiliary verb instead of sein in haben wir … überstanden?

In the German Perfekt (present perfect), most verbs use haben; sein is mainly used with verbs of movement or change of state (like gehen, kommen, sterben, einschlafen).
Überstehen (to survive / get through) describes enduring something, not moving or changing state in that technical sense, so its auxiliary is haben: wir haben … überstanden.

What tense is haben wir … überstanden, and how does it correspond to English?

Haben wir … überstanden is in the Perfekt tense (present perfect).
In spoken German, Perfekt often covers both the English simple past and present perfect, so Wir haben den Unfall gut überstanden corresponds to “We got through the accident well” or “We have got through the accident well,” depending on context.

Why is it den Unfall and not der Unfall?

Unfall is a masculine noun (der Unfall in the nominative).
In this sentence, Unfall is the direct object of überstehen, so it must be in the accusative case:

nominative: der Unfall
accusative: den Unfall
Because it’s accusative masculine, you get den Unfall.

How do I know that Unfall is masculine?

You normally have to learn the gender with the noun: der Unfall.
Some endings give hints, but -fall doesn’t have a strict rule, so Unfall is just vocabulary you memorize: der Unfall (accident). Dictionaries always list nouns with their article, e.g. der Unfall.

What is the function of gut in den Unfall gut überstanden?

Gut is an adverb modifying the verb überstanden.
It tells you how the accident was survived or endured: “we survived the accident well / without serious harm.” Without gut, it would just be “we survived the accident”; adding gut emphasizes that the outcome was relatively positive.

Could I put gut somewhere else in the sentence, and would it change the meaning?

Typical options include:

Zum Glück haben wir den Unfall gut überstanden.
Zum Glück haben wir den Unfall überstanden, und das sogar gut. (more emphatic)

You would not usually say Zum Glück haben wir gut den Unfall überstanden; that sounds unnatural.
Positioning gut right before the past participle überstanden is the default and most neutral choice.

Is überstehen a separable verb? Why is it written as one word here?

Überstehen in this meaning (to survive / to withstand / to get through) is not separable.
Some verbs with über- are separable if über- is stressed (e.g. über*setzen in the sense of “ferry across”), but in überstehen the stress is on -stehen, so über is an inseparable prefix. That’s why it stays attached and the past participle is überstanden, not *gestanden über.

Why is the verb order haben wir instead of wir haben after Zum Glück?

In a main clause, the conjugated verb must be in second position.
When you put Zum Glück (an adverbial phrase) at the beginning, that counts as position 1, so the verb must move to position 2, giving Zum Glück haben wir … and not Zum Glück wir haben ….
If you start with the subject, you get the normal Wir haben den Unfall gut überstanden.

Can I say Wir haben den Unfall zum Glück gut überstanden instead? Is the meaning different?

Yes, Wir haben den Unfall zum Glück gut überstanden is also correct and very natural.
The meaning is essentially the same; you’re just putting the comment zum Glück inside the sentence rather than at the front. The nuance difference is minimal; sentence-initial Zum Glück can sound slightly more like a comment on the whole situation.

What is the difference between Zum Glück and Glücklicherweise?

Both mean “fortunately / luckily” and are often interchangeable:

Zum Glück haben wir den Unfall gut überstanden.
Glücklicherweise haben wir den Unfall gut überstanden.

Zum Glück sounds a bit more colloquial and conversational; glücklicherweise can sound a bit more formal or written, but it’s also used in speech.

Does überstanden always mean “survived,” or can it have other meanings?

Überstanden is the past participle of überstehen, which means to get through / to survive / to endure / to withstand something difficult.
You can use it for illnesses, crises, exams, and other hardships:

Er hat die Operation gut überstanden. – He got through the operation well.
Wir haben die schwierige Zeit überstanden. – We got through the difficult time.

Could I say Wir haben den Unfall gut überlebt instead of überstanden?

You could say Wir haben den Unfall überlebt, but it sounds stronger and more literal: it focuses purely on not dying.
Den Unfall gut überstanden is broader and more idiomatic for “we came out of it okay, not too badly hurt.” It suggests a relatively good outcome, not just survival.

Why is it gut überstanden and not wohl überstanden if the English is “got through … okay / well”?

In this context, German usually uses gut to express a good or relatively positive outcome of something difficult:

die Prüfung gut bestehen / gut bestehen
die Operation gut überstehen

Wohl can mean “well” in other senses, but wohl überstanden sounds rather literary or old-fashioned. For everyday speech, gut überstanden is the standard phrase.