No, the behavior of light in the vacuum of space is not analogous to lift from suction in a void. The concept of lift from suction in a void is not a valid analogy for the movement of light in space.
In the context of the expansion of space, it's important to note that it is not the vacuum of space itself that pulls or propels light forward. Instead, the expansion of space causes the stretching of the wavelengths of light as it travels through that expanding space, resulting in the observed redshift.
Regarding your second question, the expansion of space does not pull time behind it. In the framework of general relativity, space and time are interconnected, forming a four-dimensional spacetime fabric. The expansion of space affects the geometry of this spacetime fabric, but it does not directly affect the flow of time.
It's worth noting that the concept of the expansion of space and its relationship with time is a complex topic in cosmology and general relativity. As space expands, the distances between galaxies increase, and the rate of this expansion is quantified by the Hubble constant. This expansion is often described as stretching the fabric of space, but it does not cause time to be pulled behind or altered in the same manner. Time continues to flow according to its own intrinsic nature, as experienced by observers within the expanding universe.