You can get slim range hoods that generally fit into the wall cabinets ours were approx 40cm deep which housed the complete operation, our plumber ran a 6 or so inch flexable ducting into the roof cavity and out under the eaves. Most brands make these. A photo would be helpful. https://www.thegoodguys.com.au/omega-52cm-undermount-rangehood-oru50x?CAWELAID=620013790000422290&CAGPSPN=pla&CAAGID=21711678566&CATCI=pla-376401441757&gclid=CjwKCAjw0qLOBRBUEiwAMG5xMNN63iJr0n0Bnxf31-Gt0t5s0vERt_lOwOYkC6uzovf9TDWwawry9RoCgxQQAvD_BwE&gclsrc=aw.ds&dclid=CLOv9erawdYCFc0slgodE5oLHg Where we didn't have wall cabinets we had tall boxes of stainless look laminate built up to the ceiling which contained the extraction unit, which was approx 30-40cm's and extraction ducting cheers

Yes, but are you using the gap where rangehood was to centre, or the centre of the cook top. If you have cabinetry along the wall then you can hide the fact that the extractor fan/rangehood is not centre of the cook top. Or that is how it appears in your photos.

Any range hood extractor fan would be suitable. It depends on the aesthetics of your kitchen, and your budget as to which style would suit the best. Have you thought about a down draft extractor fan?

If you are looking at ceiling cassette range hoods, then ask the supplier. Walk into an actual shop and speak to the supplier and see if they have an idea on installation cost. They may even offer a supply and install option.