In short: yes, many businesses facilitate this.

Ironically, Dutch paternity leave is only 2 days (paid), but you’re legally allowed to take something like 26 weeks unpaid in the first few years as parental leave. (Vs e.g. Sweden with 6-9 months). The law is changing to a few weeks next year I believe.

I think it differs by employer. Mine gives extra days paid leave for parents as they consider the 2 days too short (but this is uncommon) and proactively asked if I was considering 90% or 80% for the coming year, and shared how others have done this.

At my wife’s workplace there are many people with children, and the large majority works either 3 or 4 days per week.

Two weeks is common in the US; however, it tends to be all-or-nothing with regard to hours.

If you are lucky, that is. Other places will give 6 weeks at reduced pay, but many others give absolutely no paid time off for maternity leave and fewer give paternity leave. I think FMLA allows for around 4-6 weeks of unpaid time off if your employer is large enough to be covered by it. Otherwise, your results could very easily vary.

That really depends on the employer. One large US employer I know of (Cisco) offers full salary for something like five or six months, and also offers grandparent leave.