Part-time courses are permitted for a person on H-1B ... as long as you continued to work the number of hours listed on the I-129H.
Talk to your foreign student adviser for guidance on how to file the COS.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
I recommend against raising any issues which are not relevant and which you were never asked, in any application, unless you want to make your case unnecessarily complicated.
The above is intended only as general information, and does not constitute legal advice. You must speak with an attorney to discuss your individual case.
I agree with attorney Berman
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.