Is it permissible to take car and travel expenses from the mosque's funds when collecting donations for it, given the possibility of performing personal tasks that do not conflict [with the primary purpose] or sometimes failing to collect donations?

There is no objection to taking transportation expenses for collecting donations for the mosque if they are within the usual limits. This is because the one in charge of waqf funds is permitted to consume from them in a reasonable manner, based on the Prophet's (peace be upon him) saying: "There is no blame on the one who is in charge of it to eat from it in a reasonable manner, or to feed a friend who is not acquiring wealth from it." What he does during the travel does not matter as long as it does not compromise the purpose for which he traveled.