Learn Farsi: حاشیه‌های مجزا سریع تطبیق داده می‌شوند. - The separate borders are matched quickly.

Because this sentence uses the passive voice! In an active sentence, 'the borders' would be the direct object and could be fronted as a topic with را (râ). However, in a passive sentence, the original object becomes the grammatical subject. Subjects never take را (râ), even when they sit at the absolute beginning of the sentence to act as the topic.

حاشیه‌های مجزا (hâshiye-hâ-ye mojazzâ) refers to inanimate objects (borders). Why is the verb می‌شوند (mishavand) in the plural form?

While inanimate plural subjects in Farsi usually take a singular verb, using a plural verb is completely valid. It is often used in formal writing or to emphasize the individuality of the items. Here, it subtly stresses that the borders are truly مجزا (mojazzâ, separate or distinct) from one another.

How exactly is the passive verb تطبیق داده می‌شوند (tatbiq dâde mishavand) constructed here?

It is built from the active compound verb تطبیق دادن (tatbiq dâdan, to match or adapt). To make a compound verb with دادن (dâdan) passive, you keep the noun portion (تطبیق, tatbiq), change دادن (dâdan) into its past participle داده (dâde), and then add the conjugated auxiliary verb شدن (shodan, to become). For the present tense plural, that auxiliary is می‌شوند (mishavand).