Should I email old supervisor about my progress?
I just did that, and I often do. If I'm honest, I don't do that as much as I should. Anyway, unless told otherwise, which, imho, would be rare, that should be acceptable/desirable.

Of course, you won't just talk about your stuff, but ask about his/hers. You do have common interests after all. 

Professors are people too! There is no secret in talking to a fellow professional that you know. And, of course, never send a professor a lengthy message. 

Be polite, be direct, and informative...