In future if I will be unemployed and get A-kasse benefits (not other helps from kommune), does it affect my application for permanent residence? I am from a non-EU country.
Dagpenge is not a social allowance like kontanthjælp and integration allowance, and therefore it does NOT affect your application for permanent residence.
However if you later consider to apply for danish citizenship (dansk statsborgerskab), you must be aware that periods with more than 4 months with dagpenge, affects your application for statsborgerskab.