A ship powered by anti-mater would have a pretty big expolosion wouldn't it. Kind of like a nuke going off? I doubt there would be much left of a body to make an identification of it.
Of course I think its been said before, why was Kirk's mother on board the Kelven [pregnant]? This was BEFORE the time anomaly occured. It wasn't untill STNG that families were brought on board the ships due to long voyages.
During the Earth/Romulan War, Romulan ships were not powered by Anti-Matter and could only reach around Warp 2 for short periods of time before its deuterium stores were depleted..
Romulan ships of that era were Fusion Powered.... The precursor to Starfleet at that time(UE: United Earth) had just started to implement Matter/Antimatter reactors and their ships started
to take ship of the more traditional looking Starfleet vessels.. Romulan ships looked more like big mushrooms with the interior of the vessel housing mostly deuterium..
Weapons of the time were Atomic, Fusion, or conventional based on both sides of the conflict...
To answer your second question: this is just one of those things that violates its own canon throughout the whole Star Trek Saga.... In Balance of Terror, we see Specialist Martine
and Lt. Tomlinson getting married.. Ships are out on patrol or exploration missions for months, even years at a time.. They probably hadn't stopped off at a Starbase in at least 9 months..?
Logical that they would be together... After all, dating isn't forbidden Starship.. Marriage obviously isn't forbidden Starship.. I don't think sex is forbidden on Starship..
Pregnancy will happen..