A-kasse membership after leaving Denmark for 3 months
I am not fully sure if you already have graduated and now are receiving dagpenge as graduate (dimittend-dagpenge).
You are already receiving dagpenge:
If thats the case, then you are free to go to any country you like, and do what you like, as long as you remember to inform A-kasse and Jobcenter about it, and on your montly benefit registration card ("dagpengekort") you must tell that you do not wish to receive dagpenge for that period.
After you return to Denmark again you just tell A-kasse and Jobcenter that now you want to continue to receive dagpenge from where you left in the 2 year dagpenge period. So the 3 months you dont use will be added in the last end/extend the 2 year period with 3 months.
You will not loose any right to dagpenge by not having permanent address/CPR. Its not an requirement to have permanent address/cpr to be eligible for unemployment benefits. But in practice you will need it to be able to get NemID to use with A-kasse's online self-service, having bankaccount etc.
I think you can maybe keep your CPR if you only plan to be away for 3 months. But try to ask your kommune about that.
Its also important to find out if you need to change A-kasse/insurance to the polish Insurance Scheme. Normally you must change to the EU-country where you work.
Its important that you are only insured in one country at a time, and in the right country - otherwise you can totally loose your right to unemployment benefits.
In case you find out you need to be insured in Poland, then you can transfer all your rights regarding unemployment Insurance between Denmark and Poland, and again back to Denmark when you come back to Denmark.
You are still student and the intern is part of your education:
You kan keep membership with the danish A-kasse, but remember to get this confirmed by your A-kasse. You must be living in Denmark again at latest 2 weeks after graduation.
Anders Weber, www.a-kasser.dk