Learn French: Le poète ne cesse de déclamer sa prose. - The poet does not cease declaiming his prose.

This is an example of the literary omission of pas. In formal or literary French, a small group of verbs can form the negative using ne alone. The most common verbs that do this are cesser (to cease), oser (to dare), pouvoir (to be able to), and savoir (to know).

Is it mandatory to use de before déclamer?

Yes. When cesser is followed by another verb to mean "to stop doing something", it requires the preposition de plus an infinitive. It is a set structure: cesser de faire quelque chose.

Could I just say Le poète ne s'arrête pas de... instead?

Yes, grammatically that works and means the same thing, but it sounds much more conversational. Using ne cesse de without pas elevates the sentence to a formal, literary register that fits the subject of a poet perfectly.

What is the exact nuance of the verb déclamer here?

Déclamer means to recite or speak in a highly theatrical, impassioned, and dramatic way, like an actor on a stage. It adds a bit of vivid imagery (and perhaps a touch of irony) here, as the poet is passionately reciting prose (ordinary, non-metered language) rather than actual poetry.