Does your academic research capabilities during your university days count as experience specifically regarding research area?

Yes, they do. Though be carefyl about providingthe details as the partnership between your university and a client, or your university's terms and conditions might contain non-disclosure limitations. 

Best to aks for a recommendation letter from the project supervisor. 

Of course, it does. For me; these researches were the basics in building my research experience and skills. I learned how to take short cuts; to overcome my past mistakes and use better methods.

Also, its your first step you follow in your future research; you build on it, and you can use it as a reference, and what an amazing reference when you use, with your own name on; it will give you an advantage.

Finally; if you kept a data-base (your reference; books, writers, websites, surveys, .. etc) about those researches you wrote at university, it will be useful for you.

Traditionally, an internship is used to acquire academic research experience that can be added to your research profile if substantive and approved by the school as valid. During my public health training many of us conducted internships and research which was not only counted towards our academic experience but also used as a resume builder to present our research skills. In quite a few cases, students were able to obtain significant jobs based on the training they received during their internship, which is why I highly encourage internship programs in academia.

the question here is not about the information you already gathered during your research years in university, its about the capabilites, analytical skills, time management skills, organisational skills, systematic review skills, that you built during your years at the uniersity. i believe that these capabilites are of the utmost importance in your work.