Not in Berlin. It's tax free after a few years only, to prevent people from flipping houses.

Also capital gains tax is around 26% (incl. solidarity surcharge), if it hasn't changed.

However there are other scary things about house ownership in Germany. For example being liable for street work in front of your house for the first few decades. The city can decide to repave the street and stick residents with the bill.

Absolutely. I think one of the fun things about that calculator is that you can mess around with the numbers to try different situations. Perhaps there's a way to account for that tax (e.g. by using ~5.8% returns as the after-tax rate).