Sometimes a bank will release funds to an executor without confirmation. It depends on the amount held by the bank and the overall value of the estate. The bank can either decide to do so or not as the case may be. There is nothing wrong with the executor asking and the executor hasn't acted wrongly by doing so.
Irrespective of whether the bank releases funds without confirmation, if confirmation is being applied for, the bank accounts have to go on the confirmation. If the executor hasn't done this, an Eik will be needed if the banks now confirms that it needs confirmation.
Yes, the inventory is part of the application for Confirmation.