- Does the stars in clusters rotate?
Yes. All stars rotate to a greater or lesser extent whether they are in clusters, galaxies or whatever. Broadly, move massive stars rotate more (and are more often in binary systems) and there's nothing special, as far as I know, about this trend continuing in clusters.
- Does cluster's stars have moons. If yes do they rotates/orbits or are they "frozen" in space?
This question doesn't make sense. Moons don't orbit stars: they orbit planets. If you mean "Do cluster's stars have planets?" I'm not sure if we know. Given that we are currently finding stacks of planets around stars, I there are probably planets around some cluster stars but they're too far away to see (and will be for some time). And those planets will behave just like planets around other stars. They will rotate and follow an orbit. (I'm not sure what you mean by "frozen" in space?)
- What will happen if one of the stars blows up?
The main effect of supernovae in clusters is to expel interstellar gas from the cluster. That is, there are clouds of gas in the cluster at first and the fast-moving gas from a supernova blasts other gas out too. If other stars are very nearby they might be heated a bit but stars are quite hardy things when it comes to being irradiated by supernova. They wouldn't be vapourized, for example.
- Does that structure attracts or repels space objects?
Clusters would attract "space objects" by exerting gravity on them. But actually, clusters repel objects in a way. When a star in a cluster approaches a pair of stars in a binary system, the tendency is for one of the three stars to be thrown out. The cluster effectively "radiates" stars over time. Also, the above-mentioned expulsion of gas by supernova gradually depletes the cluster of mass and the stars move apart.