Is this physical and emotional response upon the mention of Allah, His verses, the Prophet's hadiths, and honoring one's parents, considered a sign that the inquirer falls under the description of "those whose hearts tremble when Allah is mentioned"? And what is the significance of the heart fluttering and feeling close to Allah sometimes during prostration?

The skins of those who fear Allah shiver and their hearts tremble when they hear the Quran and the remembrance of Allah, as stated in His Almighty saying: "Allah has sent down the best statement: a Book consistent and oft-repeated. The skins of those who fear their Lord shiver therefrom; then their skins and their hearts relax at the remembrance of Allah." (Quran 39:23), and His saying: "Indeed, the believers are those who, when Allah is mentioned, their hearts tremble, and when His verses are recited to them, it increases them in faith; and upon their Lord they rely." (Quran 8:2). The closest a servant is to his Lord is when he is prostrating. Therefore, it is recommended to ponder the meanings of the Quran, the adhkar (remembrances), and du'as (supplications) during prostration, and to frequently read books on encouragement and discouragement (of good and bad deeds), and to follow the Sunnah.