Space-Like Hypersurface: Simultaneous Events?

[Apashanka]

If two events are occurring in a space like hypersurface...is it that the two events will appear to be simultaneous from a frame moving with velocity $v\lt c$ and will appear to be occurring at the same spatially position from a frame with velocity $v\gt c$??

 

[Ibix]

If two events are occurring in a space like hypersurface...is it that the two events will appear to be simultaneous from a frame moving with velocity $v\lt c$

In flat spacetime, yes. In curved spacetime there are no global frames, and you have to be a bit more careful with your definition. It would be better to say something like that they lie in a plane whose tangent vectors are everywhere spacelike.

a frame with velocity $v\gt c$??

You cannot consistently describe such a thing.

 

[Orodruin]

Clarification: The events will be simultaneous in some frame. They will not be simultaneous in all frames.