My sister and I opened an estate account for my mother who passed away in June. How long do we need to keep the account open? How much do we need to keep in the account? We would like to close it by the end of the year to keep it in the same tax year.

If the will is probated, her estate distributed, and you are positive that all of your mother's bills have been paid off (including all final medical bills), and that there are no potential creditors lurking out there, I suppose you could close it as soon as you want.

You keep it open as long as there may be funds to distribute from it. Once all debts of the estate are paid and all inheritances distributed there is no reason to keep it open.