Yes you should include these activities. Though there are many functions of HR, it is mostly focused on the development and support of human capital within the organization. Responsibilities from your student assistant role directly correlate with HR projects and tasks. Employee recognition, helping employees advance in their career and researching best practices are characteristics that align with a successful HR department and you’ve had experience developing these skills. Be ready to articulate how your experience aligns with the job requirements in your interview. Good luck with your internship pursuit!