Is it permissible for me to manage a sum of money designated for mosque maintenance and distribution to the poor (which is relatively large) by depositing it in a bank or purchasing a car with it, then distributing portions of it monthly to the deserving and using it for mosque maintenance when needed, instead of disbursing the entire amount at once?

You must take the initiative to distribute the entire amount designated for the poor and orphans, and keep the amount allocated for mosque maintenance. You are not permitted to use it for any other purpose, whether for yourself or for others, without your friend's permission; for you are a trustworthy agent acting on behalf of your friend, and you must adhere to the limits of the agency and fulfill the trust.