1. When does the modern period in Jewish history begin? What is modernity?

According to the reading the modern period in Jewish history begins with "the onset of Modernity".  Modernity is defined as conscious recognition of an era. Modernity changed and shaped much of what was to come in the future years for Jews and people everywhere. 

6. Some Jews, among both the lower classes and the wealthy, converted to Christianity – why did they do this?

They did this for a couple of reasons.  One of the main reasons was because many jobs that were being offered to Jews were no longer being offered to them due to anti-semetic laws. If the poor people couldnt find jobs they couldnt put food on the table for their families so converting was the only option.  Some families wanted to see better days for their children so by converting they were able set their children up for the coming years.