Who is to guarantee the missing money from the fund, the manager or the assistant, after the manager gave the key to the fund to her assistant to withdraw a sum from it?

The manager is entrusted with the fund, so she is not liable unless she has been negligent. If authorizing the assistant to withdraw money constitutes negligence, then she is liable for the amount.

As for the assistant, if she was authorized to withdraw, she is entrusted and not liable unless she exceeds her authority. If she was not authorized but withdrew upon the manager's order without knowledge of the negligence, then she is not liable, and the liability falls upon the manager.