It honestly depends on the school. Personally, I RARELY had homework in apush, but my friend at a different school had 1-2 hours a night. Overall, I would recommend the class because it honestly teaches you a lot about history and it improved my writing tremendously. The only ‘homework’ I had was reading the textbook, but I’m not going to lie, I gave that up after chapter 5 (in a book with 41 chapters) and if we had a quiz over the reading (VERY rare) I would go over the corresponding notes (apnotes.net) online. We would have homework packets once every ~2 months with some practice AP multiple choice & short answer questions. The only other thing I did outside of class was preparing for dbq’s or essays we were writing in class. Again, my experience is very different than others, so really just ask students at your school who have taken the class on what the workload is like. Don’t know if it necessarily boosts application, but makes your schedule more rigorous, so that helps.