I think you already got the answer to your question, but yes, you are actually expected to be able to solve every question if you want to do well in the class.
That being said, you're not expected to be able to solve every question at the first sight. It's more likely that your professor/instructor wants you to think every question before the due date of your assignment. That thinking can take from a second to hours/days depending on your understanding of the material.
Here are some suggestions that might shorten that thinking time...
1. Read the textbook. I do understand that math textbooks are often dry and boring, but it really helps to read it, especially before the lecture since you'll get to think about the course material ahead of the time. It might be better to read the problems before the lectures as well. This might be adding your work time, but it's much helpful in the long run, and besides, I don't think reading a section/chapter in a math textbook can take that much time compared to reading a chapter in a novel.
2. Do all the easy problems first. If you got to a problem that took you 10 or more minutes of thinking, skip that question for now and come back later. You might find out that easier problems actually might help you understand the harder ones.
3. Take a break; do something else and come back later. I don't know if there is any scientific evidence to it, but I feel like it helps to work on the problem after a little bit of break can actually make me think differently, and often times that different thinking was all I needed to solve the problem.
4. Go to your instructor's office hours. There's nothing wrong with getting some help once you've actually thought about it. Most of the instructors like it when you ask questions after they have thought about the problems.
Hope this helps.