Yitz,
1. There is no such thing as certainty. In any case,Rambam states (Hilchot Melachim 3:10) that the king (= government) may execute murderers without clear proof in order to fix the world according to the needs of the time.
2. In general, a Noahide is not executed for shogeg but the goel hadam may kill him (ibid 10:1). However, there are circumstances where he is close to meizid and executed (ibid). Felony murder may well be close to meizid. The case of the fire is even more severe as starting a fire is like shooting arrows. One who starts it is liable as if he did the deed with his own hands (Shulchan Aruch Choshen Mishpat 418:17). As fora Jewish criminal, the right of a court in chutz l’Aretz to punish him is dependent on whether we consider it to be a Noahide court of a court of a partnership between Jews and Noahides (see Rav Shachter’s article on tax evasion available on-line) and if we consider it to be a Noahide court if a Noahide government court may punish Jewish criminals (the main opinion seems to be yes – cf. Rabbi Bleich’s article I mentioned). There are also opinions that government officers are like the goel hadam (ibid), which would add to the heter. An Israeli court may certainly execute him if the government would decide that the times require it (Rambam Hilchot Rotzeach 2:4 – whether the times require it is a question, Rav Yisrael Rosen says yes, Rav Aviner says no).