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

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?

For the small amount of range hood that would be in contact with the undulating subway tiles, I do not see a problem.

it does look great but it could be cheaper and definitely much easier to employ a kitchen specialist company that can coordinate this job as you will need a cabinetmaker, a carpenter, an electrician and possibly a roof plumber to install a range hood like this.. in an ideal situation if you can organise all the tradespeople together and there's no existing cabinet to remove (and walls to repair that will also need a plasterer and painter) i would expect the job to take a full day with the cabinet built off site and quickly installed but it depends on the specific needs of the location eg is there easy access to the roof space and no restriction with ceiling framing to install the exhaust flue (or can the flue be directed out the wall but how does that affect the brick walls) and where is the power and can it be redirected inside the new cabinet and??? at least obtain a quote from a kitchen company to establish a base cost but with all the different trades for several hours each plus materials plus the cost of the range hood i would expect to spend at least $3000 or more without any surprises...it's not the cabinet that costs the money it's the complex cooperation of trades and unexpected labour time that's unknown and i would not attempt to start without coordinating the whole team needed to do the whole job