Since the grail is corrupted, it is possible to skirt the rules and summon a servant using the grail as long as they are not a proper one. This was the loophole that Caster used to summon Sasaki Kojirou, who more of a wraith then a heroic spirit, in canon. Beelzebub used the same loophole to summon Jack, who is also a wraith, especially since he is way better at summoning then Medea.

: She was interested in the grail wars since the second one, especially since Artoria appeared, but she didn't actually intervene until Gilles appeared and only much later, like when Lancelot jacked a freaking plane. Beelzebub counters her in the same way as Zouken, as even though his bugs are more spiritual they are still bugs and counter her illusions. He will just camp his bugs near the airports like Zouken.

Not really, since the only reason she wanted to go in the first place was because Gilles appeared in the war, and with their being Beelzebub instead, she likely not show up. Or will she?