Hi,
1. Important regarding graduates and A-kasse are the time up to the start of your education and the time right after finishing your education.
So you must meet the following two conditions for being able to get benefits as an graduate:
-You had a permanent address in Denmark no later than one day before the start of your education.
-You are in Denmark no later than 14 days (including weekends) after you end your education.
But it is NOT necessary to stay in Denmark DURING your study, so there is no problem with the Erasmus exchange. During your stay abroad you can continue the free membership with the danish A-kasse.
2. You can only have free membership as long as you are studying. As soon as you graduate you must begin to pay the normal price, like you say around DKK 500 per month.
3. I am not sure I fully understand your third question - but you can receive dagpenge for up to two years, with
possibility to extend the period with up to 1 year more.
You can earn right to the extended period by working.
We have described these rules in details here.
You receive the graduate rate DKK 13,489 every month for the 2 year/3 year period, as long as you pay the monthly membership fee to your A-kasse, and off course are unemployed.
There will be no additional fees or withdrawals period if you leave the A-kasse. And You will not be asked to pay anything back of the dagpenge you have received during your unemployment period.
Best regards,
Anders, www.a-kasser.dk