Here’s a suggestion: http://www.suncoastsheetmetal.com.au/cms/index.php/domestic/kitchens.html

there are several range hoods eg Miele that can be vented horizontally and even some that can vent downward under the floor and another that has the motor outside the walls but you'll need to check with manufacturers to clarify which one would suit as you need to know exactly where the wall and floor framing is located to make sure there's enough space for installation ..rear venting rangehoods don't use less cabinet space they just avoid having a pipe through the ceiling and roof...

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?