Do all objects fall at the same rate? and if they do not why?

No, I heavier object will fall much faster than something lighter than it. This is because it's more dense and hard so it can cut through the air particles quicker than a lighter object which takes longer to cut through the air and fall

Example:

A rock vs a feather

The rock will fall quicker because it's more dense and falls straight down and the feather will be slower because it flows slowly down through the air particles