More than likely. Indonesian has borrowed quite a bit from Arabic since it's a muslim-majority nation.
Yes, you are right, like "koran" related to the arabic "quran" (newspaper). Because majority people in indonesia is moslem.
I always thought it was dutch (krant) and in Afrikaans we say koerant, although I can't seem to find any information on "koran"'s word origin
In this case, "kuat" may probably be a stative verb, meaning it's a verb that denotes a quality of being ("to be strong"), rather than an action. So, the copula "to be" isn't needed. As far as I know, there are lots of stative verbs in Indonsian, which in English would just be adjectives.
I gather no copula is used, at least not in informal speech. Is it used in more formal speech?