Understanding Grammar and Syntax

• Familiarise yourself with the intricacies of Hindi grammar and syntax. Remember, precision in usage is what sets an expert apart from a novice.
• A deep understanding of verb tenses, agreement, concordance and cases underlines effective Hindi usage specifically in the spoken format.

Use of Correct Conjunctions and Word Order

• Perfect the use of conjunctions. These hold sentences together and significantly improve the flow of content.
• Hindi, unlike English, follows a Subject-Object-Verb (SOV) word order. Preserve the structure in your phrases and sentences to keep your language comprehension clear and accurate.

Noun Cases and Declensions

• Hindi employs cases and declensions for nouns and pronouns. A systematic knowledge of these declines and how they modify nouns is important for the correct use of grammar and syntax.
• The specific case endings are critical for clear and precise meaning of your sentence.

Grammar Rules: Tenses and Aspect

• Hindi verbs carry information relating to number, gender, tense, phase and mood, and include conjugations that English doesn't necessarily use. Mastering them can greatly enhance the preciseness of your speaking.
• Hindi also maintains specifics with regards to aspect. This is a grammatical category that determines how verbs relate to the flow of time. Grasping this concept can greatly improve both your understanding and effective use of Hindi.

Prepositions and Postpositions

• Proper use and understanding of postpositions in Hindi is key, as they take the place of prepositions in English.
• In Hindi, the postpositions follow the word they relate to, which impacts the sentence's meaning profoundly, so focus on getting your postpositions correct.

Correction and Self Assessment

• Evaluate your speech – correct the grammatical errors, syntax discrepancies and work consistently to minimize them.
• Regular self-assessment can aid in the steady improvement of your grammatical accuracy and syntax precision. Practice speaking Hindi frequently and in varied contexts to assess and improve your language skills.

Nuances and Culture-Specific Syntax

• While adhering to the grammar rules, remember to incorporate regional and cultural nuances. It's these small touches that can make your Hindi sound more natural and fluent.
• Also, understand the influences of culture on syntax and how they change based on where the language is spoken. Adding some of these elements can greatly enhance your conversations and presentations.