What is a fully declining ism (munṣarif)?
This is the ordinary ism, and there are far more of these than of anything else.
مُسْلِمٌ / مُسْلِمًا / مُسْلِمٍ — ḍamma, fatḥa, kasra, each with tanwīn. Add الـ and the tanwīn goes, leaving the bare vowel: الْمُسْلِمُ / الْمُسْلِمَ / الْمُسْلِمِ.
Every ism falls into one of three: fully declining, partly declining, or non-declining. The category decides how the i'rab is expressed — not what the i'rab is.
One writing rule comes with it. When a munṣarif ism is indefinite and in nasab, an alif is written after it — كِتَابًا, رَجُلًا — with two exceptions: a word ending in ة takes none (جَنَّةً), and a word ending in اء takes none (سَمَاءً).
Two warnings. Tanwīn does not mean singular — a broken plural takes it too: كُتُبٌ. And a word is munṣarif by default: it takes only one thing to stop it, which is the subject of the next page.
Like most Arabic grammar terms, صَرْف (ṣarf) was taken from everyday speech and then given one precise technical sense.
In everyday Arabic it means turning or changing a thing about.
صَرَفَ النَّظَرَ (ṣarafa al-naẓara) — “he turned his gaze away”
In Arabic grammar it means the free turning of an ism through all three endings with tanwīn. An ism that has it is munṣarif; one prevented from it is mamnū' min al-ṣarf.