1) to start with I must correct you. You will get 1 month waiting period. Its not a quarantine - the quarantine is correctly 3 weeks and is given to people who for example are self-inflicted unemployed.
But for graduates there are this special 1 month waiting-period, if you have not been member of A-kasse for less than 1 year when graduating.
So answer to your first question is that you will get paid first time October 31 for the full October month. You will have waiting period for the full september.
If your waiting-period goes from middle of a month, you will get paid first time off course for a 1/2 month. There is howevever a minimum amount/hours that an A-kasse pays dagpenge for. You must have right to receive at least dagpenge for 14.8 hours for a month, otherwise you will not receive any money that month.So if for example your waiting period starts on the last day in a month, then you will not get paid for 1 day in the next month.
2) You can work up to 145.53 hours per month if you want to have supplementary benefits ("supplerende dagpenge"). A normal full month in Denmark is 160.33 hours, but since there is a minimum amount/hours that the A-kasse want to make a payment for, then there is a rule saying that everything less than 14.8 (160.33-145.53) hours per month is not paid.
You can get supplerende dagpenge for up to maximum 30 weeks. Supplerende dagpenge is calculated on week-basis but paid out on monthly basis. You will use 1 week of supplerende dagpenge everytime you write some working-hours (less than 37 hours) on your montly registraion-card ("dagpengekort") in the A-kasse.
The weeks with supplerende dagpenge is deducted in your 2 year period with dagpenge. After 30 weeks you must decide whether you want to continue your part-time job with no supplementary benefits or you want to stop the job. If you stop the job you can continue to receive dagpenge in the rest of the 2-year period.
The hours you have worked during your period with supplerende dagpenge can be used to extend the existing 2-year dagpenge-period. It is extended in the way that 1 hour work gives two hours more dagpenge.
You can also choose to use the working-hours to try to earn a new 2-year period with dagpenge. A new 2-year period requires 1,924 working hours or income of DKK 238,512 during the last 3 years. Only income from last time you started a dagpenge-period can be used.
Anders Weber, www.a-kasser.dk