Generally speaking, it is the responsibility of the fiduciary appointed by the Court (i.e. executor, administrator) to be in charge of the estate bank accounts. Banks and financial institutions will need to see certificates of Letters Testamentary which grant the authority to the executor to conduct estate business, including the ability to open an estate bank account.
Before you open the estate bank account, you will need to obtain a tax identification number (EIN), which can be easily obtained through the IRS website (irs.gov). Once the estate account is opened, you will receive starter checks, and eventually, a regular checkbook with a series of estate checks for paying estate expenses and making distributions to estate beneficiaries and legatees.
While the executor should be entrusted with the estate checkbook, they should consult with the estate lawyer regarding the payment of estate expenses to ensure that it is truly an expense of the estate, and not a personal expense or an expenses for other purposes that fall outside the purview of the estate. Obviously the lawyer should be consulted before distributions are made to beneficiaries as it must be ensure that all estate debts have been paid and that proper distributions are made to the beneficiaries. This is where the experience of a qualified estate administration attorney comes into play.