The atomic weaponry was probably retconned by Enterprise's use of phasers and torpedoes.
The problem with the Romulans not being seen prior to Balance of Terror, a fact that Enterprise seems to try to maintain, is the line where Spock says the ships from the time of the war were primitive in a way that didn't allow captives. It might make sense if the ships at the time lacked any means of docking with each other. This could be explained by use of long-range fighters, which use fewer crew, instead of starships. And these fighters may have been equipped with atomic weapons for use against installations rather than use against starships...
The other explanation I came up with could be a modification of Valdore's plan to use remote guidance on the Romulan ships used in the war. Rather than needing something like a telepathic operator, the plan may have been simplified to remote control of individual vessels, with most of the ships' systems being automated.
As far as the singularity usage time frame question, I don't think it was in operation by the time of Balance of Terror, as the Romulan ship had nuclear detonators on board to self-destruct. If they had a singularity core, which would likely have to be kept near the evaporation point to be useful, they could either have shut off any kind of matter stream and destroyed the ship that way, or shoved enough matter into it to overwhelm whatever containment method is used and swallow the ship.
What got me started on this topic was watching a horribly-played Let's Play of Star Trek Legacy, where the final mission of the Enterprise era has the Enterprise blowing up old Vulcan stations with nuclear cores to disable a large number of Romulan ships. I kinda liked the idea that those ships would supplement Earth Starfleet and the nascent Federation for a while, since I don't think Earth had that many ships at the time and their fleet size likely doubled as a result of that mission. And yes, I do know that entire storyline is non-canon, but it raised an interesting problem that hadn't been solved on-screen yet.
