I am Jewish on my mom's side of the family.
Some pretty common Jewish names are Rachel, Esther, Rebekah (Yes it is spelled like that), and Josephine. The most common in my family is Esther we have 7 women in my family named Esther.
My family's surnames are Barrocas and Bernstein but there are many good Jewish Surnames.
Yes this tradition is called the Shiva. If you just google you will get a vast amount of information about it.
Jewish Day schools? I have no idea. I am sorry I can't help with that one.
Good luck with your project and research will be vital in your project.
Hope I helped a little.