I was also going to mention the Romulan Quantum Singularity drives as an alternative to the matter/antimatter reactors used by the Federation. We never really get to hear what other races use for their energy sources, but I wouldn't rule out anything, even ZPE.
As far as needing a compact reactor, even shuttles as small as the Type 6 had a warp drive. The much larger Runabouts and the Delta Flyer also had advanced warp drives. I'm not sure what the absolute smallest warp-capable ship would be, but the tech is certainly there.
I'm not sure of the rationale behind not having fighters in Trek, because from a tactical standpoint it would seem to be the superior method of interstellar battle (multiple attack vectors, minimized casualties, etc). If I had to guess, either Roddenberry or the other producers were trying to distance Trek from Star Wars, where battles were primarily carried out by compact fighters.
I personally would love to see Federation fighters, even if they weren't solo craft and required additional pilots/nav/tactical crew. Fighters was one of the things that made Battlestar Galactica exciting.
As far as what time period, its only a guess but I would say the technology already exists in the current cinematic time period, so we're talking late 23rd century (what year are we up to now in the prime universe, 2390-91?)
I believe the rational for no fighters in the Trek Universe is that the larger capital ships have higher warp potential than the smaller craft, there seems to be economies of scale that allow those large ships to reach those higher warp numbers than is possible for smaller craft, that is why my fighter uses an alternate power plant than the typical Matter/Antimatter design, I'm assuming antimatter storage is bulky and more easily done in larger ships, and the matter/antimatter reaction chambers require shielding to protect the crews from the radiation released. The fighter's zero point energy cells release less stray radiation and thus require less shielding to protect the pilot.