Sorry if the title doesn't accurately describe my problem, I am new to Stack Exchange. I need to make all the faces move up equally, but the ones circled in yellow only move up half way, while the ones in red are how I want them to move. This has happened to me multiple times with different models and I am trying to find a solution
Your problem comes down to changing the internal triangulation done by Blender, as described by Robin Betts here: flipping internal triangulation
In your particular case: select problematic faces, Ctrl + T to triangulate, change Quad Method to Fixed Alternate, select the new edges and dissolve them:
If you want to make a script automatically fixing such quads, this could be a starting point: Select concave quads
The best solution is proportional editing. Press 'O' or that little icon on the top highlighted in the image below. Then when you move a vertex you will see a circle around the vertex you have selected. The size of the circle is controlled by the scroll wheel on a mouse. The bigger the area the circle is, the more strongly the other vertices will move with that single vertex.