How to ask for another university prof for course materials?
It is definitely not a mistake to ask the instructor for his course notes. From what I know it is common practice to do this and many professors and grad students do this on a regular basis even if you are not a student taking that course.
I would recommend you take a straightforward approach, there's no need to beat around the bush. Introduce yourself to the instructor being clear about your intentions with his course notes. If there are some certain parts of the course you are more interested in, remember to mention them as they might be more comfortable sharing some parts of the content rather than the whole thing.
An EDU email could be better but it depends on the circumstances. If you are a professor teaching  a similar course at some other university, the instructor might have his concerns regarding sharing content but if you work in industry and there's no chance of stealing their work they might be okay with sharing it.
If they don't answer you can drop another email after some time (I usually give people a week before sending a polite reminder email). However if you don't get a reply for your second email, I personally wouldn't keep sending them emails.

I hope this was helpful. Let me know if you have any more questions.