It seems to be Teak, which is a quite expensive wood. Lots of Yachts and Boats are made of Teak and it is used widely on decks, so, I still dont understand what your question is? What you are saying, is that because of the electrical and AC Vent, you need to drop the ceiling? Do you have straight walls/ceiling? can the wood be attached to the existing ceiling? The Carpenter installing the wood, could just lower the AC Vent and what kind of electrical are you talking about? The ceiling can lights?

yes, you can do a coffered look like the pic I've put up. This was done with MDF and 2-piece crown molding.

Hello, You may have to remove them , take them to nearest timber get them planed and then reinstall. after planing you may have to buy few additional pieces to cover up the material lost in planing. Otherwise, If the gaps are not very big you can try filling them with metal paste or wood putty.

hey you can go for pvc false ceiling, they are durable and have many design options. you can also install bronze glass if you would like a different touch to the room.