What else can he do? If he admits to dick pics then surely that's 100% he has to stand down. Perhaps he's trying to pay her off.
The
actual story (in German) from Bild is here. Bild are a trash tabloid, about equivalent to
The Sun but I don't think they'd publish such claims without verification they can at least point as being credibly reliable. They'll be keen to avoid any libel claims if nothing else. Of course, pics aren't necessarily dick pics but that seems more likely than anything else.
I don't think it will be. The investigation is being handled by the parent company, not the F1 team, and they have too much on the line to let it slide.