There are a few possible explanations for why your student(s) can't post. First, the student(s) might not be in a group. Go to the Participants page (Course Dashboard > Participants) and scroll to the student. It should list the group(s) they are in under the Groups column. If they are not in a group, click the pencil next to "No groups" and select the desired group from the dropdown. Then click the Save icon on the right. If they are in a group, did you set the appropriate grouping in the forum settings? If not, do so. If you do have it set to the appropriate grouping, it might be that the groups are not associated with that grouping. For either, please see our help guide on how to Create Groups and Groupings.
The other possible explanation is that you set your forum type to the Q&A Forum Type, but did not post any questions. When using a Q&A Forum Type you, the instructor, must post first. You are posting the "question." Students then come in and reply to your question with their "answer" (hence the name Q&A). Students cannot post questions, so if there are no questions posted, students are unable to post in the forum. Question posts are not brought over when importing or restoring course content, so they will need to be re-posted each term. You must post the question to each group for the students to be able to answer.
Yes, you can create a group assignment using the Assignment activity. A group assignment means when one member of the group submits, the submission is applied to all group members. And when you grade, the grade and feedback is given to all group members.
When you set up the Assignment, you will enable group submissions in the Group Submission Settings section. See the Group Submissions Settings section in our help guide on how to create an Assignment for more information.
You will need to create the groups within your course before they begin submitting to the group Assignment. Please see our help guide on how to Create Groups and Groupings.