I've added pretty much every phrase from homework to home assignment, it should work now
washing dishes, mowing the lawn, dusting, laundry, cooking, lol. If I were in school I wouldn't have any time left for homework.
Домашня робота can mean both: homework and all that home stuff (washing dishes, mowing the lawn, etc)
Home task? Home task? Home task? :D
Never heard it, sounds so strange... Just plain old homework as in, assignments at school... Not housework...
Oh, no, that's different.
Завдання = task, assignment. Домашнє завдання = homework (given at school)
Задача = problem (in Maths). Математична задача = Maths problem