Medelinor The first question: After entering the translations in the “Weblate”, what is required of me after that in order for the translation to be applied?
It takes about 1 hour to export translations from Weblate to language pack. But you may need to use composer require "flarum-lang/arabic:dev-master"
command to install it (by default Composer installs only tagged versions, which probably will not contain your new changes).
Medelinor The second question: I want, for example, to insert translations for my own forum (which contain phrases that may not apply to other Flarum forums), is there a possibility for that?
You may take a look at this blog post: https://rob006.net/en/blog/how-to-change-or-add-missing-translations-for-flarum/