most codes say 30" to combustible surface like a decorative wood hood over cooktop. the metal style hoods can be a little less but keep in mind your eye level & also how far the hood projects as you don't want to get bopped in the head every time you are cooking. the typical 6" high hood are generally 63" to underside with overhead cabinet about 69" floor to underside.

Wow your ceiling must be really, really low then ? Most extractors have to have a gap between 650mm to 760mm between the bottom of them and the hob part of the cooker - so in your case the lid should have clearance even if set at standard height, even if it’s an over depth appliance. What height is the ceiling ? Is the cooker going right into the corner ? Might be useful to have it 150mm from the corner,so you have a small clearance for pan handles on the left. If you’d like me to look over your plan to safety check it - I’ll happily do that for free - just email me if you don’t want to post it publicly on here.

We used to have a similar one in our previous kitchen. Didn’t have a hinge, had to remove the front panel to get access to the filter. The hole point of these things is that they give you head space while cooking, so they are supposed to be ‘closed’. Just keep it closed and only open it to clean it. Looks really nice.

If you do opt to have a chimney extractor, neff for example have chimney extensions of 750mm for taller ceilings for some of their extractors. The chimney can easily be cut to allow for the sloping ceiling by a competant kitchen installer, I've had to cut down many chimneys when I was an installer. Your kitchen designer should be able to advise you the different options you have though for your extractor and a high ceiling.