Yes, part-time studies (“Teilzeitstudium”) are possible.
The master program does not offer itself preparation classes for german. But the Humboldt-Universität zu Berlin offers courses as “German as a Foreign Language” in the Language centre. These courses are booked out very quickly.
There are several possibilities outside the university, for example Goethe Institut here, which is much more expensive than in most other countries. Volkshochschulen offer a cheaper way. And of course there are a lot of private schools which offer german courses.
There is no general online option for the Master in Statistics. Due to the COVID-19 pandemic currently all teaching is done online, but this will change as soon as the pandemic is over/under control.
Yes, if you apply for admission, you have to a approve that your level of German is at least B1. Which documents are valid, can be found under “Spezielle Kenntnisse 3” in the program specific admission rules (German: Fachspezifische Zugangs- und Zulassungsregeln des Master Statistik).
The mandatory course Stochastik I is in German but almost all others courses are held in English.