Can a nuclear reactor be used as a space-based weapon? Imagine you have a ship, running on power from a nuclear reactor. We will assume this ship uses some kind of advanced technology that allows nuclear reactors to function in a microgravity environment.
This ship is a in critical state, having fought 3 alien ships at the same time. The nuclear reactor is going critical, so the captain wants to eject it and have it crash against an alien ship. Crashing the ship itself is against his good judgement, as he wishes to give his crew a chance to survive.
We shall assume that in such a split second decision, it is impossible to calculate detonation timer and it is too late to fit a proximity or remote detonator onto the nuclear reactor.
Now my question:


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*If the critical nuclear reactor crashes against an alien ship, will it achieve the same devastating effect as a nuclear weapon (as seen in Battlestar Galactica, for example)?

*If this happens in the orbit of Earth, will it have any effect on those on the surface, or will it simply be turn into harmless microwaves?

 A: If you're imagining some kind of colossal explosion from the nuclear reactor, then this won't happen unless some kind of "make me into a bomb if you throw me at alien ships" feature is expressly designed into the reactor. 
The reason is that bombs and reactors work very differently. The main problem that must be solved in a bomb is that as the chain reaction begins, the huge amount of energy released tends to blow everything apart, thus the critical mass swiftly becomes uncritical, thus putting a very swift end to the reaction. Contrary to popular beliefs, if you put two less-than-critical chunks of bomb fuel together to make a more-than-critical mass, you would not get a bomb. The chunks would blow each other apart in microseconds, you might get a bang that scatters a few of your desk items asunder and you will drench every living thing nearby in a lethal dose of neutrons. But you most certainly won't get a big bang. Exactly this scenario claimed the life of Harry Daghlian during the Manhattan Project: he died, in hospital, 25 days afterwards of radiation induced injuries. The supercritical mass was wholly an accident: he accidentally dropped a neutron-reflecting tungsten carbide brick onto his experiment, making the core he was working on supercritical.
To make a bomb, huge forces from a chemical explosion either assemble a critical mass very quickly or, with a precise, inwardly converging spherical wave, crush a below-critical mass enough that it becomes supercritcal by dint of its crushed, significantly smaller volume. The key point: the large forces from the chemical explosion and momentum of precisely designed containers contain and uphold criticality for enough time for enough fuel to undergo fission to let slip bomb-type energy magnitudes. Otherwise everything blows apart quickly and the explosion is not much bigger than the chemical explosion alone.
As you can see, reactors are not designed like this. If the reactor becomes dangerously supercritcal, reacting too fast, it is simply going to scatter itself very swiftly. You'll get poison, but not a big bang. Shards and gunk from a thrown reactor could be a nasty radiological weapon (i.e. a great big ball of radioactive poison), but this is not going to disable your foe very quickly. It would only be a final tactic of revenge to avenge the lives your now dead crew.
A: Let's assume that there is a "shadow shield" protecting the ship from the nuclear reactor, this means that the shielding is only in the direction of the rest of the ship (protecting the crew while saving weight). When the unshielded, uncontrollable, reactor hits the enemy ship, the radiation will kill everything on board. The reactor will not explode, however, it will probably glow white hot as there is no air to convect the heat away.
The effects on the ground would be minimal, as there would be no fallout and radiation would be negligible due to the inverse square law.
Note: There already are nuclear reactors that can operate in microgravity: SNAP-10A, NERVA, RORSAT, SAFE.
