Learn Hardcore German: Zum Glück habe ich eine zweite Stirnlampe im Rucksack, sodass wir den Pfad zurück zum Campingplatz finden. - Luckily I have a second headlamp in my backpack so that we find the path back to the campsite.

The finite verb (here: habe) must be in second position in the sentence.
The first position can be the subject or some other element (time, place, adverbial, etc.).

Here:

First position: Zum Glück (an adverbial phrase)
Second position: habe (the verb)
Then: ich (the subject)

So Zum Glück habe ich … is correct.
Zum Glück ich habe … breaks the verb‑second rule and is ungrammatical.

Why is it eine zweite Stirnlampe and not ein zweites Stirnlampe?

Because Stirnlampe is:

A feminine noun: die Stirnlampe (singular), die Stirnlampen (plural).

That affects both the article and the form of zweite:

Case: It’s the direct object of habe, so accusative.
Gender: feminine.
Indefinite article, fem. accusative: eine.
Ordinal number zweite behaves like an adjective and must agree: zweite (feminine accusative).

So:

eine zweite Stirnlampe = a second headlamp.

Ein zweites Stirnlampe is wrong because:

ein and zweites are the forms for neuter (or masculine in some cases),
but Stirnlampe is feminine.

What is the nuance of zweite here? Does it mean “a second one” or “another one”?

zweite literally means second (in an ordered sense: first, second, third …).

In context, though, eine zweite Stirnlampe is often understood as:

a second headlamp / one more headlamp, so functionally very close to another headlamp in English.

Subtle difference:

eine andere Stirnlampe = a different headlamp (not the same one as before).
eine zweite Stirnlampe = a second headlamp in addition to the first one.

In this sentence, zweite emphasizes that there is one more headlamp available, which saves the situation.

What exactly does Stirnlampe mean, and what’s its gender and plural?

Stirnlampe is a compound noun:

die Stirn = forehead
die Lampe = lamp

So die Stirnlampe literally is a forehead lamp, i.e. a headlamp / head torch.

Grammar:

Gender: feminine – die Stirnlampe
Plural: die Stirnlampen

Like most German nouns, it’s capitalized. In compounds, the last part determines the gender, so because Lampe is feminine, Stirnlampe is feminine too.

Why is it im Rucksack and not in dem Rucksack? And what case is that?

im is just the contraction of:

in dem → im

This is very common and usually preferred in speech and writing.

Case and gender:

Rucksack is masculine: der Rucksack.
The preposition in with a location (where something is) takes the dative.
Masculine dative singular of the definite article: dem.

So in full:
in dem Rucksack → contracted: im Rucksack.

You could also say:

in meinem Rucksack = in my backpack
The German sentence simply omits the possessive; context often makes ownership clear.

What does sodass mean, and how is it different from damit or deshalb?

sodass introduces a subordinate clause of result / consequence:

…, sodass wir den Pfad … finden.
= … so that / with the result that we (are able to) find the path back …

Comparisons:

sodass: emphasizes the result / consequence of what was just said.
damit: emphasizes purpose / intention (on purpose, in order to).
- Ich nehme eine Stirnlampe mit, damit wir den Pfad finden.
  = I take a headlamp so that / in order that we can find the path.
deshalb / deswegen / daher: are adverbs, not conjunctions; they don’t create a subordinate clause.
- Ich habe eine zweite Stirnlampe, deshalb finden wir den Pfad.
  (main clause + main clause)

In spelling, sodass (one word) is the standard modern form; so dass (two words) is still accepted but less common.

Why does the verb finden go at the end of the part sodass wir den Pfad zurück zum Campingplatz finden?

Because sodass is a subordinating conjunction (Subjunktion).
Subordinating conjunctions send the conjugated verb to the end of the clause in German.

Structure of the subordinate clause:

sodass – conjunction
wir – subject
den Pfad – direct object (accusative)
zurück zum Campingplatz – adverbial phrase (direction)
finden – conjugated verb, final position

So:

Main clause: Zum Glück habe ich eine zweite Stirnlampe im Rucksack,
(verb in 2nd position)
Subordinate clause: sodass wir den Pfad zurück zum Campingplatz finden.
(verb at the end)

This verb‑final order is standard for all subordinate clauses with words like weil, dass, wenn, obwohl, sodass, etc.

Why is it den Pfad and not der Pfad?

Pfad is:

Masculine: der Pfad (the path).

In this sentence, den Pfad is the direct object of finden:

We find the path → the path is what is found → direct object → accusative case.

Masculine definite article:

Nominative: der Pfad (subject)
Accusative: den Pfad (direct object)

So den Pfad is correct because finden takes an accusative object.

How does zurück work here? Is zurückfinden one verb, or is zurück just an adverb?

In this sentence, zurück is used as a directional adverb: back.

den Pfad zurück zum Campingplatz finden
= find the path back to the campsite

There is also a separable-prefix verb zurückfinden, but its meaning leans more toward “find one's way back”:

Wir finden zurück zum Campingplatz.
= We find our way back to the campsite.

In this sentence:

The verb is simply finden.
zurück zum Campingplatz describes where / in what direction: back to the campsite.

So here zurück is not glued to finden as one fixed verb, it just modifies the action like back in English.

Why is it zum Campingplatz and not zu dem Campingplatz or nach dem Campingplatz?

zum is the contraction of:

zu dem → zum

Grammar:

Campingplatz is masculine: der Campingplatz.
zu with a direction towards something takes the dative: zu dem Campingplatz.
Contraction is very common: zum Campingplatz.

Choice of preposition:

zu is used for movement toward places, especially when you think of a specific place / spot / institution:
- zum Bahnhof (to the station)
- zum Arzt (to the doctor)
- zum Campingplatz (to the campsite)
nach is used mainly with cities, countries, and “home”:
- nach Berlin, nach Deutschland, nach Hause.

So zum Campingplatz is the natural way to say to the campsite here.

Why is there a comma before sodass? Is that always required?

Yes, here the comma is required because sodass starts a subordinate clause.

German comma rule:

You must put a comma between a main clause and a subordinate clause, and also between coordinate clauses in most cases.

Structure:

Main clause: Zum Glück habe ich eine zweite Stirnlampe im Rucksack,
Subordinate clause: sodass wir den Pfad zurück zum Campingplatz finden.

Therefore, the comma before sodass is mandatory according to standard German punctuation rules.

The English translation would often say “so that we can find the path back”. Why is können missing in German?

German often omits modal verbs like können when the possibility / ability is already implied by the context or structure.

…, sodass wir den Pfad … finden.
literally: “so that we find the path back …”
but the meaning is “so that we can find the path back …”.

Adding können is possible:

…, sodass wir den Pfad zurück zum Campingplatz finden können.

Both are correct. The version without können is shorter and very idiomatic, and the concept of being able to is understood from context.