There is no approval needed:

• up to 2 days continously: I say I am sick, I am put on sick leave. I had to do this already the 3rd time this year (thx German weather)
• from the 3rd day, I need to bring a paper from the doc. If the doc says I’m sick, I’m kept on sick leave as long as the doc requested
• vacation days are independent from sick days: I get 30 paid vacation days, so 6 weeks