Rambam, הלכות סנהדרין פרק י"ג: Once the verdict [of death] has been rendered, [the convicted] is executed without delay on the same day.
There is very little time between the verdict and execution, there is not much time for Mitzos. Rambam doesn't mention whether he does וידוי or קריאת שמע before death. In chapter 13:2, Rambam adds that one who confesses is given a bit of Frankincense mixed with wine to befuddle his mind (שתטרף דעתו עליו וישתכר), and put him into a drunken state, presumably to numb the pain of execution. I would infer from these הלכות that Mitvos are pretty much irrelevant from the point of conviction onward.
Regarding loss of possessions: Although Rambam also writes that the relatives of the convicted do not mourn him after death (13:6), it doesn't say anywhere that the condemned loses his possessions. I have never seen anywhere stated that there is any monetary penalty accompanying the death penalty. On the contrary, the Gemara states that someone who is liable to a monetary penalty or lashes, and also the death penalty, only gets the death penalty.
A rationale for this: We usually speak of the death penalty as atonement, not punishment. So no other penalty is required to atone for the convicted. Therefore the court has no need to take his possessions, and they will pass to his heirs, as in a normal death, since the execution is sufficient for atonement.