a) Various sources suggest that Gehinom, Purgatory, is a physical place, somewhere deep beneath the earth's surface, where the souls of the wicked are punished.
Nachmanides (Rabbi Moshe ben Nachman 1195-1270) writes:
"These and other similar matters cannot be interpreted as a parable or as some ominous saying. The Rabbis specified its location and the length and width of its dimensions. They consider [the heat generated by Gehinom] in the context of Jewish law."
Notwithstanding the sources above subscribing to and depicting Gehinom as a physical place, other sources -- in Kabbalah, Chassidut, and Jewish philosophy -- portray Gehinom in more abstract and spiritual terms. In fact, later, as Nachmanides continues his above mentioned exposition on Gehinom, he seems to do an about-face, also explaining the fires of Gehinom and the punishment endured by the soul in spiritual terms.
The discrepancy, however, between the various depictions of Gehinom can be reconciled based on the mystical concept that reality has manifold layers. So although the mystical dimension of Torah focuses on the higher reality, including the underlying spiritual reality and dynamics of Gehinom, the revealed dimension of Torah speaks about the physical manifestations of reality within the context of the here-and-now, the tangible and the palpable. This explains why our Sages have said that a Scriptural verse always retains its simple meaning, even while each and every verse alludes to the most exalted of mystical concepts.
According to Judaism, the purifying process that a sullied soul undergoes to cleanse it from its spiritual uncleanliness is a temporary one, and is restorative in its intent, and not punitive, as many mistakenly believe. Ultimately, all Jews have portion in the World to Come, as do Righteous Gentiles, non-Jews who observe the Seven Noahide Commandments.
b) According to Torah, no spiritual force opposes G‑d. This includes Satan, who is a spiritual entity that faithfully carries out its divinely assigned task of trying to seduce people to stumble. Satan is also identified with the Prosecutor above -- that's what the word Satan itself means: it's just Hebrew for prosecutor -- who levels charges against the guilty party who succumbs to its wily arguments. Look in the beginning chapter of the Book of Job and you'll see that clearly.
In fact, the Talmud says, all that Satan does, he does for the sake of heaven. Without him, the defense attorney wouldn't bother to dig up all the merits of the defense. And the defense would have to try so hard to give himself more merits.
So you see that really nothing happens in the entire world without G‑d approving. That's why we Jews have so many complaints to him that we need to talk to him three times a day. The buck really stops at His office.
Finally, when the Divine Court decides that someone, G‑d forbid, deserves to die, then Satan is dispatched from Above to carry out the sentence.
Rabbi Eliezer Danzinger for Chabad.org