Possibly, but it would all depend upon how powerful the engines were and if they needed any extra fuel (like single H). Right now, of course, we don’t have any high powered nuclear engines that could even be considered for the task. Then, of course, you’ve got the issues of people worrying about what would happen if the thing broke up on take off or reentry.
You lost me. How would a nuclear engine provide propulsion? The current method is to use a reaction engine, a rocket, which requires reaction mass to expel at high velocity to get forward thrust.
What does a nuclear engine do?
Currently, the nuclear powered spacecraft we’ve built, like Voyager, Pioneer, and Cassini, use the nuclear material like a battery to power an emitter which shoots out electrons to propel the probe. It’s slow, but it’s constant, so over time, the speeds can build up. NASA is researching improved technologies using ion power for their Prometheus Program The hope is that one day, we’ll be able to build something which can successfully compete with chemical rockets.
The other type of nuclear engine is the nuclear thermal engine, where a nuclear reactor is used to directly heat a propellant and eject it through a nozzle. This can probably be used for a launcher.
Even with such an engine, I think a fast reentry with aerobraking would still be preferable. Nuclear rocket engines still require propellant. And Columbia accident notwithstanding, heat shields are generally more reliable than rocket engines.

Currently, the nuclear powered spacecraft we’ve built, like Voyager, Pioneer, and Cassini, use the nuclear material like a battery to power an emitter which shoots out electrons to propel the probe. It’s slow, but it’s constant, so over time, the speeds can build up. NASA is researching improved technologies using ion power for their Prometheus Program The hope is that one day, we’ll be able to build something which can successfully compete with chemical rockets.
I thought so. Such a system works for spacecraft that are exploring the far reaches of the solar system and have months, or years, to gain speed. I don’t see it as a way to answer the question posed by the OP of braking the shuttle to a slower speed in order to reduce the heat load on reentry.

The other type of nuclear engine is the nuclear thermal engine, where a nuclear reactor is used to directly heat a propellant and eject it through a nozzle. This can probably be used for a launcher.
Even with such an engine, I think a fast reentry with aerobraking would still be preferable. Nuclear rocket engines still require propellant. And Columbia accident notwithstanding, heat shields are generally more reliable than rocket engines.
And, again, wouldn’t it take about as much propellant to get down as it did to get up and the getting-down propellant would take up all the space and weight allowance that is needed in order to have any payload at all.