Learn Hardcore Russian: Ветреный день у моря был приятным.

Adjectives like ветреный (windy) are built from the noun ветер (wind) plus the suffix -ен-, and Russian spelling rules say that adjectives with -ен- take just one н. Double нн appears in participles (e.g. заключённый) or adjectives formed with suffixes -енн-/-онн-.

What’s the difference between ветреный and ветряной?

Both come from ветер but have distinct meanings:

ветреный means “exposed to wind, breezy” (a windy day, a fickle person).
ветряной means “powered by wind” or “related to wind” (a windmill = ветряная мельница).
You wouldn’t call a day ветряной, but you would speak of a ветряная турбина.

Why do we use был here? In present tense Russian often drops the verb “to be.”

In modern Russian you can drop есть (“is”) in the present tense, but in the past (and future) you must use the appropriate form of быть. So “The day was pleasant” needs был for the past tense.

Why is приятным in the instrumental case, not the nominative приятный?

After a past-tense linking verb like был, a predicate adjective goes into the instrumental case to show the state or quality of the subject. Hence день был приятным, not приятный.

Why is у моря used, and why is море in the genitive case?

The preposition у (“by, near, at”) always governs the genitive case in Russian. у моря literally means “by the sea” or “at the seaside.”

What’s the difference between день у моря and день на море?

день у моря – “a day by the sea,” i.e. on the shore.
день на море – “a day at sea,” often implying you’re actually on the water or at a beach resort.
Context decides which preposition you choose.

Where are the English articles the or a in this sentence?

Russian has no articles. Definiteness or indefiniteness (the vs. a) is inferred from context, word order, intonation or added words (e.g. этот – “this”).

Can we change the word order? What if we say У моря был приятным ветреный день?

You can reorder for emphasis but must keep grammatical agreement.

У моря был приятным ветреный день sounds awkward because it separates the adjective приятным (instrumental) from день (nominative).
Better: У моря был ветреный и приятный день or Ветреный день у моря был приятным (neutral).

Could we use the adverb приятно instead of the adjective приятным?

Yes, but it changes the structure to impersonal:

Днем у моря было приятно. (“It was pleasant [to be] by the sea in the daytime.”)
Here приятно is an adverb describing the general feeling, and there is no explicit noun “day” as the grammatical subject; the construction is impersonal.