to make things clear....for being eligible for unemployment benefits ("dagpenge") you must be a member of an A-kasse. However you do not need to member of an Union. A-kasse and Union are two different things.
If you were staying in Denmark just before you started your AP and stayed/stay again in Denmark at latest 2 weeks after graduation, and you also sign up for membership in an A-kasse at latest 2 weeks after graduation, then you are eligible for unemployment benefits ("dagpenge") after the special graduate rule.
As long as you meet these requirements then it is not relevant if you have been studying some semesters and/or have had internship outside Denmark.
You tell you are an EU-citizen, so I assume that you meet the residence requirement, i.e. have stayed in Denmark or another EU-country for at least 5 out of the last 12 years (in 2019).
You do not need to have a CPR, neither you need to have your own accomodation (it is ok to stay with a friend). However, you must expect that the A-kasse may require some kind of proof of your residence right before starting education, and again now.
Anders Weber, www.a-kasser.dk