Is it permissible to save money with the intention of donating it on behalf of one's parents and a friend, then give it to the poor after a few days or weeks, or must the intention be made at the time the money is given to the needy? And is it permissible to intend the charity on behalf of all Muslims?

There is no objection to saving money with the intention of giving it as charity on behalf of one's parent or anyone else and disbursing it later. It is not obligatory to disburse it immediately upon forming the intention. The intention at the time of setting the money aside is sufficient, as the general rule is that intention should be concurrent with the act of worship. However, jurists have explicitly stated that the intention at the time of setting the money aside is sufficient for ease, especially since voluntary charity is less stringent. The intention is sufficient if it is known at the time of payment that it is charity. Similarly, there is no objection to giving charity with the intention that it be on behalf of all Muslims.