Is it permissible to add some letters to words in the Holy Quran, or to write "سينين" (seenin) instead of "السلام عليكم" (peace be upon you) with the addition of the alif, and is the writing of the Quran divinely ordained?

The orthography of the Qur'an is divinely ordained and specific to the writing of the Mushaf and what pertains to the Qur'an itself. As for writing verses for the purpose of citation or when quoting the style of the Qur'an, there is no harm in writing them phonetically or omitting a letter from them. Some scholars have permitted those proficient in Arabic to use some verses in compositions, letters, and speeches, and to alter their grammatical structure.