Is it permissible for the mosque's imam, who is entrusted with collecting and distributing zakat, to take a share designated for those who work on it, knowing that his monthly salary is for his role as an imam and not for his work with zakat?

It is permissible for the Imam appointed by the ruler to collect zakat to take what the ruler gives him in return for his work, as he is among those "employed to collect zakat." However, it is not permissible for him to take anything from it without the ruler's permission, because that is a betrayal of trust.

As for the Imam who is a volunteer and not appointed by the ruler, it is not permissible for him to take from the zakat, because he is an agent for the owner of the money in its distribution and not among those "employed to collect it."