On the left hand side you can also look up sex offenders.
From what I can tell, the only restrictions to where a sex offender can't live are schools, so answer to #5, is no, this does not include churches.
And as for #3, no they DO NOT have to tell you they moved in. On the link above, one of the questions answers how you CAN be automatically notified if a sex offender moves into the neighborhood by requesting to be added to a list.