"time is an illusion... lunchtime doubly so..." - Ford Prefect.
Since we haven't had much impact outside the planet, I expect the impact of the earth "vanishing" would be very little at all. After all "space is big... really big!"
As for different species perceiving time at different rates, it is a tantalising idea, that's been explored in many sci fi books (and probably shows
). Terry Patchett explores it well in the Discworld books. It makes sense that a sloth would perceive time more slowly than a little bird like a robin, finch or a wren. But as to proving it... I don't know how to start...
Al.