WI Princess Vicky and Crown Prince Fred had head aches the night Bill was concevied in otl or she had a misscarriage
Who would rule Germany?
Likely Henry or Sigismund, Wilhelm's younger brothers. Or, possibly, an ATL variant of Wilhelm himself, hard to tell with butterflies and naming conventions.
How powerful could Bismark stay?
He'd likely get dimissed either way. He might stick around for a few more years, but he was getting old and he wasn't lacking in enemies.
Does Germany keep a good relationship with the Czar?
Possible, but unlikely. German and Russian strategic interests tend to conflict and there was pressure to break the alliance OTL from both sides. It wasn't just Wilhelm's work (quite the opposite, Wilhelm and Nicholas did at one point put together a declaration of friendship entirely in private ... that both their Empires' Foreign Ministries quietly swept under the rug as counter to their nations' interests).
In retrospect, sure, Russia would be a better ally than Austria, but choosing the Eastern Hordes over a fellow Germanic power at the time would be political suicide, even for an Emperor.