Fjällstugan låg nära vattenfallet.

Because Swedish very often forms compound nouns by joining words together.

• fjäll = mountain, fell
• stuga = cottage, cabin

So fjällstuga means mountain cabin.
Then the definite ending is added to the whole compound:

• fjällstuga = a mountain cabin
• fjällstugan = the mountain cabin

This is extremely common in Swedish.

That -n is the definite article suffix, meaning the.

In Swedish, the is usually attached to the end of the noun instead of being a separate word before it.

• en stuga = a cabin
• stugan = the cabin
• en fjällstuga = a mountain cabin
• fjällstugan = the mountain cabin

So fjällstugan literally means the mountain cabin.

Because Swedish usually expresses definiteness with an ending on the noun.

So instead of saying something like the mountain cabin, Swedish says:

• fjällstugan

And instead of the waterfall, Swedish says:

• vattenfallet

This is one of the biggest differences from English.

Låg is the past tense of ligga.

• ligga = to lie, to be situated, to be located
• låg = lay / was situated / was located

In this sentence, låg does not necessarily mean the cabin was physically lying on its side. For places and buildings, Swedish often uses ligga to mean be located.

So Fjällstugan låg nära vattenfallet means that the cabin was situated near the waterfall.

Swedish often prefers ligga for the location of buildings, places, and areas.

Compare:

• Stugan låg vid sjön. = The cabin was by the lake.
• Stockholm ligger i Sverige. = Stockholm is in Sweden.

Using vara is possible in some contexts, but ligga often sounds more natural when talking about physical location.

So låg gives the idea of was located rather than just was.

Yes, they look the same, but here låg is a verb form, not an adjective.

Two different things:

• låg as adjective = low
• låg as verb = past tense of ligga

In this sentence, it must be the verb, because it is describing what the cabin did / where it was located.

Nära means near or close to.

Here it works as a preposition:

• nära vattenfallet = near the waterfall

Unlike English, you do not need an extra to after near in Swedish.
So Swedish says:

• nära vattenfallet

not something like nära till vattenfallet.

It is another compound noun:

• vatten = water
• fall = fall

Together:

• vattenfall = waterfall

Then the definite ending is added:

• ett vattenfall = a waterfall
• vattenfallet = the waterfall

So the sentence uses two compounds: fjällstugan and vattenfallet.

Because vattenfall is an ett-word (a neuter noun), not an en-word.

Swedish nouns usually belong to one of two groups:

• en-words
• ett-words

For definite singular forms:

• many en-words take -en
• many ett-words take -et

So:

• en stuga → stugan
• ett vattenfall → vattenfallet

That is why the two nouns have different endings.

The word order is very straightforward:

• Fjällstugan = subject
• låg = verb
• nära vattenfallet = adverbial/prepositional phrase

So the pattern is:

Subject + verb + place expression

This is the normal order for a simple statement in Swedish.

Yes, that would be understandable, and in some contexts it can work. But låg is usually more natural when talking about where a building or place was located.

So:

• Fjällstugan låg nära vattenfallet = more idiomatic for location
• Fjällstugan var nära vattenfallet = understandable, but less specifically about physical location

A learner should get used to Swedish using ligga very often for places.

The dictionary form is ligga.

Important forms are:

• ligga = infinitive
• ligger = present
• låg = past
• legat = supine/past participle form used with har

Examples:

• Stugan ligger nära vattenfallet. = The cabin is near the waterfall.
• Stugan låg nära vattenfallet. = The cabin was near the waterfall.
• Stugan har legat nära vattenfallet länge. = The cabin has been near the waterfall for a long time.

A few words may be tricky for English speakers:

• fjällstugan: the fj can be difficult; many learners approximate it as something like fyell-
• låg: the å is a rounded vowel, somewhat like the vowel in British law
• nära: the ä sounds somewhat like the vowel in air in some accents, though not exactly
• vattenfallet: notice the double tt, which signals a short vowel before it

You do not need perfect pronunciation immediately, but it helps to notice that Swedish spelling often gives clues about vowel length and consonant length.

Because nära is not agreeing with the noun the way an adjective would here. It is functioning as a preposition/adverb, and in this use it stays the same.

So you simply say:

• nära huset = near the house
• nära sjön = near the lake
• nära vattenfallet = near the waterfall

No extra endings are needed.