Hello Amy,
Your struggle of whether or not to accept invitations to connect is normal. Without institution policies, I advise people to use their personal judgement since the institution has not provided guidance. I personally look at the following variables when connecting: Do I truly know the person? If I don't know the person, are they transparent with why they want to connect? Is it clear from their profile that we have commonalities? Does the person requesting a connection have a complete profile (lack of a complete profile means unwillingness to disclose and I don't accept)? With students, again, it is a personal choice on whether one feels comfortable accepting or having their own "policy" of only accepting graduate requests. I accepted requests only when students had profiles that aligned with career center instruction on how to optimize their profile. I used this as a means to help students with their profiles before accepting requests and personally felt that if a student was engaging, it was a good idea to accept requests and coach them on LinkedIn through online interactions and through the content shared via my feed (such as articles on tips for interviewing, etc.). These are some things to consider when there are no policies to provide guidance.
To answer your question regarding course length, one enrolled, participants have 4 weeks to complete the course so you have a month. This is why it is key to make sure that once you enroll, you have actually set aside time to focus on learning and interacting just as one might do with an online college course. However, The Lounge (www.careercollegelounge.com) is our post-course informal learning platform that allows you to continue interacting and engaging for the sake of further learning. I am responsive to all who participate in the Lounge just as if they were leaving comments in a course forum so we can still interact there as well. There are also some downloadable resources provided in this course to allow participants to deepen their understanding of the content and to provide guidance. Don't worry - I'll still be around to assist even when the course is complete and would be happy to further engage with you via the Lounge.
Robert Starks Jr.