You need to be represented by counsel to probate an estate in Florida. In addition, if you cannot notify an heir by mail and cannot located them, you will have to petition the court for alternate methods of notification.
If there are no available funds because no one can access the estate account, get a new executor appointed as soon as possible. In the meantime, the beneficiaries should advance the expenses. It's cheaper than having to pay penalties and late fees.
This does not sound right. However, if the child is a minor, she is not able to enter into a contract not to sue. If she is now of age, she should retain other counsel to review the matter and possibly contest the accounting.
Not all assets go through probate so this may be legal. For example, life insurance benefits go directly to the beneficiary. Many investment accounts have beneficiary designations. A house can be titled in joint ownership with rights of survivorship, so it also does not pass through probate. The same is true of a car. So if you want to make sure that everything is listed accurately, you may need to retain your own counsel to double check.
You need to consult with a probate attorney to review the decedent's assets and determine whether they pass through probate. A corporation has a life of its own and does not go through probate. The same is true of an LLC. However, the decedent's interest in these entities may be subject to probate. you need to determine if the entities or members had buy-sell agreements determining disposition of the ownership interest upon death.
The terms of the will have no bearing on the P.O.D. account. Unless the beneficiaries of the P.O.D. account were joint beneficiaries, the bank can require that your deceased sister's estate be probated. This is not as daunting as it sounds, as you may be able to do this by a small estate affidavit and conduct the whole process by mail.
If probate was never opened, the issue is who was awarded the house in the will? Also what was the value of the property at the time of death? Depending on these answers your mother may have to open probate or you may be able to transfer the property by affidavit. You definitely want to consult with a probate attorney.