Is the interpretation correct that Moses’s dispensing with his staff, which was of utmost importance to him, and his trust that Allah would compensate him with something better, is true?

The questioner should improve the terminology used, as the meaning intended by "blind trust" is better expressed by "reliance on God" (tawakkul), "submission," or "having a good opinion of God" (husn al-dhann billah), all of which are legitimate Islamic terms conveying sound meanings. A servant's Islam cannot be firm except through submission and surrender to Allah, which necessitates avoiding dispute and objection. All objections must be repelled with the conviction that Allah is All-Wise and All-Knowing, and that sound reason does not contradict authentic revelation. The meaning the questioner understood from the noble verse (فَأَلْقَاهَا - so he cast it down) is correct. Moses, peace be upon him, thought that Allah commanded him to reject the staff, and whoever gives up something for Allah, Allah replaces it with something better. The letter "fa" (فَـ - so) in (فَأَلْقَاهَا - so he cast it down) indicates Moses' swift response to his Lord's command, which is how a Muslim should be when dealing with the commands of Allah and His Messenger, without hesitation or procrastination. The questioner is advised to refer to simplified Qur'an commentaries to ponder the meanings of the verses.