The answer to each of these questions is yes. In fact at Illinois about 40-50% of the students in each of these courses consist of newcomers.
I am now in my last semester at the U of I and will be graduating with highest honors. I have never felt I was hurt by taking a C&M class versus a traditional style class. On the contrary, I think it has helped me immensely. While other Electrical and Computer Engineering students were getting bogged down in math, I was able to apply my Mathematica knowledge and C&M skills to concentrate my attention to understanding the core Electrical and Computer Engineering issues.
Techs support both the lab machines and the software used in this program.
In the event of a problem, send an e-mail to tech@cm.math.uiuc.edu.