Learn Polish: Ledwo weszliśmy w ciemność, jedna latarka zgasła. - We had barely entered the darkness when one flashlight went out.

In English we say "had barely [done X] when [Y happened]", but Polish simply puts the two clauses side-by-side with a comma. The word ledwo (barely) at the start of the first clause is enough to connect the two events. Both verbs (weszliśmy and zgasła) are in the past perfective tense to show one completed action immediately followed by another.

Could I use ledwie instead of ledwo here?

Yes, ledwie and ledwo are completely interchangeable in this sentence. They both act as conjunctions of immediate anteriority, meaning they show that the second event happened the very moment the first one finished.

Why is it w ciemność (accusative) instead of w ciemności (locative)?

We use the accusative case here because the verb wejść (to enter) implies motion into a destination. If there were no motion and you were just standing in the dark, you would use the locative case (w ciemności). Because ciemność is a feminine noun ending in a consonant, its accusative form looks exactly like its nominative form.

Why does the sentence use the perfective verb zgasła rather than the imperfective gasła?