1. Attached are some pictures of our joints in the bathroom, what could have gone wrong there?
The tiler worked very poorly, such joints are unacceptable, with holes in them. Tip on the side: Nowadays it is mandatory to apply a waterproof coating under the tiles in the bathroom, I would suspect that this was not done either.
2. Corner trims are partially rusty and very sharp-edged.
Also very poorly done here, it is better not to set corner trims at an angle. I still don't think it is rust, but just badly cut off because it got too hot, not even deburred, I would not pay fully for these pieces.
3. Floor tiles in the hallway please look at the differences, is that acceptable porcelain stoneware 30×60?
Depending on how you interpret the photos: Depending on the price/quality of the porcelain stoneware (from €40 /m² this should be excluded) the tiles have a banana shape, nothing can be done about that by the tiler. But it could also be that too much grout has been washed out, but those are rather minor details.
4. Why are my joints so different in color? They should be dark grey.
This is the expansion joint, a good craftsman would inform the customer that silicone comes in different shades of grey and let them choose the one closest to it. But again, rather minor details. But be careful! I have never been directly involved with the trade of tiling, except that I watched my tiler over his shoulder during my house construction and informed myself when buying tiles.