By law, is an executor of a living person rquired to give an account yarly

You will have to provide an accounting if the will requires it.  If it doesn nt, the beneficiaries can still request it through the court.  If it is your father in law's spouse that passed away, and he inherited her assets, then the estate is closed, and you can be operating more as a power of attorney, if your father in law gives you that authority, instead of an executor.  You should probably discuss this with an elder law attorney.