A packet is given on Friday that is due the next Friday; they typically include Math, Grammar, and Reading.
Our two 4th grade homeroom teachers and two 5th grade homeroom teachers all teach both grades.
Yes, some subjects have finals at the end of the school year. The 5th graders take an on-level and off-level math final to help determine their placement for 6th grade (along with other data).
It depends on the subject area; they receive math homework every night.