Learn Farsi: با این تلقین، دانشجو را رخوتی سنگین گرفت. - With this suggestion, a heavy lethargy overtook the student.

This is the core of the Accusative Experiencer Construction you are learning. In Farsi, involuntary physical or psychological states often catch or take the person. The person experiencing the state takes the object marker rā, while the state itself (roxvati sangin) acts as the grammatical subject of the verb gereft.

I expected 'a heavy lethargy' to be roxvat-e sangini, but here it is roxvati sangin. Why does the indefinite i come before the adjective?

Attaching the indefinite i directly to the noun before the adjective is a slightly more formal and literary structure than putting it at the very end of the phrase. Both mean exactly the same thing, but roxvati sangin matches the somewhat elevated, descriptive tone of this sentence.

Does talqin mean suggestion in the sense of recommending something to a friend?

No, it is not used for everyday recommendations. talqin specifically refers to psychological suggestion, hypnosis, or deeply instilling an idea into someone's mind. In this sentence, planting that psychological suggestion is what triggers the involuntary physical state.

The object dānešju rā comes before the subject roxvati sangin. Is this word order required for this construction?

It is not strictly required by Farsi grammar, but it is the most natural and common word order. In experiencer constructions, the person feeling the state is the central focus of the sentence. Placing the experiencer before the grammatical subject highlights who is being affected.