I'm using push and pop matrix and wondering, "why isn't there a way to push: fill/nofill, fill color, stroke/nostroke, strokecolor, strokeweight, rectMode and other modes.

You have pushStyle() and popStyle() for do all these attributes in one go.

 Are rotations in radians?

Yes and you have two functions to convert between radians and degrees.

1. radians(angle_in_degrees); // returns number of radians
2. degrees(angle_in_radians); // returns number of degrees
   

With regard to your questions on matrices, they may seem simple but unfortunately the answers are not. Basically Processing provides two classes for matrix manipulation PMatrix2D and PMatrix3D and these can be used to perform rotation, translation and scaling for 2D and 3D graphics.This article discusses the use on rotation matrices in 2D which will explain why the matrix has six values.

Using these matrices directly is hard work and Processing provides methods such as translate, rotate, scale which when called will update the transformation matrices for you.

The identity matrix defines a matrix that will translate by zero, rotate by zero and scale by one. It holds the initial starting values  that the transformation matrix will use at the beginning of the draw() method.