Can I sue the Executor of the Estate for negligence, damages, and fraudulent charges to the Estate and the account of the Estate?

You could have several claims here. 

First off it sounds as if there is breach of fiduciary duty either through fraud or negligence.  A fiduciary relationship is one founded on trust placed by one person in the integrity of another.  Out of such a relation, the law raises the rule that neither party may take selfish advantage of his trust, or deal with the subject-matter of the trust in such a way as to benefit himself or prejudice the other.  An example of fiduciary relations would be that of executor and heir.  A fiduciary must exercise the utmost good faith and put his interests beneath the interests of the other party.  The failure of a fiduciary to perform his duties properly may give rise to a claim. 

While such a claim may stand alone, it is often brought in conjunction with claims such as misconduct of an executor.  An executor of an estate owes a duty to exercise his obligations in accordance with the Will under which he was appointed.  The executor must also follow the law as it pertains to the distribution and handling of the assets in the estate.  Failure to perform the obligations of executor in an appropriate manner may give rise to a claim for the misconduct of the executor.

Based on your on the facts as you presented, you need to see an attorney in your area.  It's unfortunate that this involves your grandmother but the estate needs to be protected.