When it was a possibility, what was the minimum age to receive the death penalty? Was it 13?
The Midrash (Bamidbar Rabbah 18:4) explains that instead of the Heavenly Court, the Court Below can impose such a penalty from thirteen years old:
An emissary of the court on high only imposes a penalty [on people] from the age of twenty years, while the court below [only imposes a penalty] from the age of thirteen years. (emphasis mine)
Rashi, in his commentary to Numbers 16:27 explains that the Court Below does not punish a person before he shows signs of puberty. Thirteen years old is the age in which the Torah considers a person to be a man and not a child anymore (see Avos 5:21 with the commentary of the Bartenura)
See also this comment on a earlier post.