I want to change the height of a rectangle bottom - top from 0 to 1080px starting from position -1080 to 0. How do I do that? By default the transform does not have a size. It does have a scale but it's blurring out the edges when I'm trying to do the same with it.
Why not just start with a full screen square and simply position it off the bottom of the frame. You can then simply animate it moving up. Even if you have something on the square, it will generally look better to slide in than stretch in. If there isn't anything on the square, it will look the same either sliding or stretching in if I understand your scenario correctly.
First it's important to know which version of After Effects you use. It might be different from one version to another. But in general all parameters of an element can be changed over time. If when you select an element there is a small stop-clock you can select to change this parameter for different positions in your timeline. When you activate the stop-clock you can change the position, height and so on for every point in you timeline. It's very hard to explain this just by words. You can learn using AfterEffects best by watching some tutorials on YouTube ;)
If you're working in an HD comp (1920x1080), and create a rectangle that fills the screen,then a horizontal scale of 100% equates to 1920, and a vertical scale equates to 1080.
I think you might be having a problem with your anchor points. If you want to scale from one corner of a rectangle, then you need to move the shape's anchor point to a corner before you scale it up or down. Have a read about the "pan behind" tool.