Each assignment belongs to a course and lesson, so from the Assignments menu you need to first select course and lesson. Then you can create assignment for it.
This is pretty simple – just write the requirements you have and the students will be able to submit their solutions. There is an option to allow file upload as a solution to assignment.
Note that by default assignments are optional. If you want a homework to be approved before the associated lesson can be completed, you need to select the assignment in the Edit Lesson page.
Every user with privileges to administrate the LMS can review and approve or reject assignments on the lessons.
Where can admin find the submitted solutions?
Assignments -> select course and lessons and you’ll see link under View solutions.
Is it possible to output assignments as a part of a lesson page, not as a link? If not, is it possible to avoid using a pre-formatted table?
You can use the namaste-assignments shortcode. See the internal Help page for details.