What is the ruling on a congregant who precedes his imam in rising from the second prostration after his sitting for a short rest? And should the congregant remain silent if he finishes reciting the surah while the imam is still prolonging his recitation in the first silent rak'ah?

There is no blame upon you for standing up due to your assumption that the Imam had raised, as you did not intentionally oppose him. You should not return to prostration as long as the Imam has left it, and you are not obligated to return to the sitting of rest (jalsat al-istiraha). It is recommended for the worshipper in a silent prayer, if he completes the surah (definition) after Al-Fatiha before the Imam bows, to increase in recitation, or to recite a second and third surah, until the Imam bows. This is better than standing waiting for the Imam's bowing without any dhikr. If the worshipper does not recite anything and remains silent, or busies himself with supplication until the Imam bows, there is no blame upon him.