you ask about about different subjects:
1. Can i transfer my unemployment rights to Denmark?
Yes, when you are EU-citizen you can transfer your rights, but in Demark we have these special condition you must meet for having right to transfer unemployment rights:
- you must apply for membership of an danish A-kasse within 8 weeks after you ceased to be insured in another EU country (Greece).
- And further there is the requirement that you within the 8 weeks must begin work in Denmark of at least 296 hours over 12 weeks / 3 months.
but you can not get benefits in DK at the same time you are studying - se next answer
2. Can I get benefits from DK and do my master at the same time?
No, according to the danish rules about unemployment benefits, education is considered as/compared with "work" - so therefor you can not get benefits during your study. But there is special favourable rules for graduates to get benefits right after study is finished.
Until recently there was a special practice regarding PhD students who were employed as paid PhD students: they were regarded as a PhD student from the day they no longer received salaries - and that they then as students could receive benefits while they completed their PhD part time. This practice is changed/stopped with a new law from december 2016.
So it is no longer possible to complete a Ph.D. as a part-time study while receiving unemployment benefits.
3. Masters or unpaid PhDs are accepted education courses?
Yes, If you take your master or phD in Denmark and the period of study is at least 18 months (3 semestre) you can get benefits as an graduate after finish master/phd.
Though, please remember these requirements:
-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, i.e. you must apply for membership within two weeks (14 days) of completing your education.
We have an article (currently only in danish) targeting PhD and Unemployment benfits/A-kasse. See it here.
During your master/phD study here in Denmark you can become free member of an A-kasse. This way you will avoid the 1 month quarantine after study before you can get benefits. Read more about free study-membership and avantages.