Installing under the cabinet exhaust hood. Need pointers on duct work!

Hi guys,



We're installing a new under the cabinet range hood. And it's my first time doing any sort of duct work, so I definitely need some pointers.



Here's my old set-up.



Here's my new, empty area with the planned furniture placement:





This is the new range hood:





... and the cabinet that will be placed above it:





And here's what's left of the old duct work. This part is sticking out of the ceiling:





A few questions:

• Was my old ductwork done properly? I was hoping to model my new set-up after the previous one. But of course, I want to make sure that the old ducts appear to be done up properly!


• I haven't hanged my cabinets yet (they're IKEA's SEKTION line). Is it easier to hang the cabinet, then drill the duct holes? Or is there a better order to do things?


• How does duct-sizing work? My old ducts appear to be 6" diameter. Do you just buy a bunch of 6" duct pipes and just tape them together (kind of like ABS plumbing pipe)?


• How do I connect my new duct piping to the old bit sticking out of the ceiling? Just use tape?


• If my ducts aren't a perfect fit for my planned areas, can I just cut them down to size?


• What type of tape is best to use? My online research seems to show that aluminum foil type is superior to duct tape.


• Does the range hood itself get screwed into the drywall? Or into the bottom of the cabinet that it's connected to?

I know that I just threw a lot of questions onto here, so I thank you all in advance for your patience and help with this!

Installing under the cabinet exhaust hood. Need pointers on duct work!