if we have a wave in space is it necessary that it travels at speed of light?

Yep. You cant have any other kind of wave in free space except electromagnetic, and it travels at c.

No. It depends on the boundary conditions. If you have a microwave guide, technically the wave travels in the vacuum inside the wave guide but the actual velocity depends on the shape of the wave guide and the frequency of the wave in a very complicated manner.

If you have no boundary conditions (or "free" boundary conditions), the answer is yes, the electromagnetic wave will always travel at the speed of light.

what sort of wave?

a cheery wave?

a wave whipped up wind?

a head touching forelock type of wave?

or an electro-magnetic wave which only travels at the speed of light