NTRs are basically open-cycle gas cooled reactors. The thermal limit on the reactor temp is when does stuff start to melt. Project Rho[0] suggests that's the reactor temp anyways. But you need to be able to separate out the oxygen from the thermolysis stream, rather than just feeding the entire thing into your engine, both because your Isp would go to crap if you tossed the oxygen out too, and you'd have oxidizing your reactor problems. Though, you could just store it all as ammonia, and you get more hydrogen for your buck, and can probably just feed that all through the reactor.
Right. In a NTR the nuclear fuel has to be hotter than the hydrogen (or ammonia or methane or whatever) propellant so that the heat energy from the first conducts to the second. In a combustion energy the fuel and the propellant are the same substance so you try to limit conduction and can end up with propellant much hotter than the engine.
[0]:http://www.projectrho.com/public_html/rocket/enginelist2.php