Two questions

First is, is Miller generally a Jewish name, or is it one that can be
both Jewish and Gentile? I thought I have
seen some Jews carry that name, but growing up, I often seen it on
Gentile families.

The second is about Jews not being able to use something that was made
on Shabbos. I think I vaguely remember
something about that. Am I close on that, or do I have my wires
crossed? I have a follow up question with regards
to the internet if I am close.