Learn Hardcore Swedish: Hunden är nästan alltid lugn.

Swedish marks definiteness by attaching a suffix to the noun. hund is “dog,” and adding -en (the definite common-gender ending) yields hunden (“the dog”). There is no separate article like the in front.

Why is the adjective lugn not lugnt or lugna here?

Adjectives in Swedish change form depending on gender, number, and position. After the verb vara (to be), adjectives are in their predicative (uninflected) form for singular common-gender subjects: that form is lugn. If you had a neuter noun you’d say lugnt, and for a plural subject you’d use lugna.

What does nästan alltid mean, and why is nästan placed before alltid?

nästan is an adverb meaning “almost,” and alltid means “always,” so together they mean “almost always.” In Swedish, degree adverbs (like nästan) usually precede the adverb they modify (like alltid).

Why is nästan alltid placed after är instead of before the subject?

Swedish main clauses follow the V2 rule, which means the verb must be the second element. Here the first element is the subject hunden, the verb is är, and everything else (including adverbials like nästan alltid) follows.

Can you move nästan alltid to the beginning of the sentence?

Yes. If you front nästan alltid, you keep är in second position:
Nästan alltid är hunden lugn.
It’s grammatical but changes the emphasis towards how often the dog is calm.

Could you drop the verb är and say Hunden nästan alltid lugn like in English?

No. Swedish requires the copula är to link subject and predicate. Omitting it would be ungrammatical.

How would you say “The dogs are almost always calm” in Swedish?

You’d pluralize both noun and adjective:
Hundarna är nästan alltid lugna.
Here hundarna is the definite plural of hund, and lugna is the plural predicative form of lugn.