You take a separate additional sick leave as a parent with a sick child in Germany. Working from home is something the employee can do to mitigate his absence. Each parent gets 10 days per year with one kid and up to 25 with multiple kids. If you are a single parent it doubles, so 20 for one kid and up to 50 for 2+ kids
edit: kids up to the age of 12.
edit2: it can be unpaid. However you get sickpay instead.
We dont have grocery bagers. I assume you mean people whos sole income are tips? Thats not legal here. You can tip the pizza guy and waiter, but they are employees getting a paycheck from their employers. Tips are a bonus for a job well done and unrelated to them making a living.
Part time with a fixed schedule works the same way.
With flexible hours the average working hours per day are calculated. So if you work for 40 hours a month, a sick day gets you around 2 hours of sick leave.
edit: I think I got you now, you mean day labor, who get payed for how long they can work for changing employers?
I had to google for that, those are "Unständig Beschäftigte". Those are people who are employed for less then a week. They dont get sick leave. I couldnt tell you an example where it is allowed to hire someone like that. Even field workers/harvest helper get a normal contract with predefined working hours.