Hi,
1) you are right about that you can not get unemployment benefits (fulltime or supplementary) in the 6 months job-seek period. This is because you are not allowed to take any fulltime-job with one day notice. You are only allowed to search for job and work 20 hours per week. It is also a condition for the study-permit that the student is self-supporting throughout the stay in Denmark. Therefore, if you only have a normal study-visa you will not be able to get Unemployment benefits.
If you get a full-time job, you will need to apply for working permit.
2) If you are under the establishment card scheme you are not allowed to get unemployment benefits as graduate. But you can earn right to unemployment benefits like other wage-earners. This means you have to be member one year and meet the income-requirement. Read more about the requirements here: https://www.a-kasser.dk/benefits/. This also means that the last option you mention in your post is not relevant. You can not get unemployment benefits as a graduate if you seek for establishment card.
Remember always as a non-EU citizen: it gives only meaning to pay for A-kasse if you are sure that you can stay and work (fulltime) in Denmark, in case you lose your current job/become unemployed.
We do not guide about work-permit – you must find out your self if you have the right work-permit. SIRI, https://www.nyidanmark.dk/en-GB/ContactUs/Contact%20SIRI is the right place to ask about work-permit.
Let me know if you need more help.
Best regards,
Anders Weber, A-kasser.dk