I'm trying to get a package deal for new tyres and I am considering going same all around.
Does it affect handling and steering for the worse?

The rim width is different front to rear by half an inch, I believe, so I also wonder if the 245s will even fit properly..

 

With my 3-season setup, I've got 245/40 ZR19 tires in the front, mounted on 19x8.5" wheels with a +32 offset. Everything is fine.

Rears are 275/35 ZR19 on 19x10" wheels with a +42 offset.

Car is lowered conservatively, with just enough neg camber to make things flush.