The wavelength of a wave in a waveguide can be greater or smaller than in free space, depending on the dimensions of the waveguide and the operating frequency.
In general, for a given frequency, the wavelength in a waveguide is shorter than in free space. This is because the waveguide constrains the wave and forces it to propagate within a limited space, which effectively reduces the wavelength. The relationship between the wavelength in a waveguide and in free space depends on the specific design and dimensions of the waveguide.
As for the second part of your question, I'm not entirely clear on what you mean by "free space velocity" and "space velocity." The speed of light in free space is a fundamental constant denoted by "c" and is approximately 299,792,458 meters per second. It is the maximum speed at which electromagnetic waves can propagate in a vacuum. The velocity of light in a waveguide, on the other hand, depends on the properties of the waveguide, such as its material and dimensions. In general, the velocity of light in a waveguide is lower than the speed of light in free space. However, it's important to note that the velocity of light in a waveguide is not inversely proportional to the speed of light in free space. The relationship between the two velocities is more complex and depends on the specific characteristics of the waveguide.