"We would like to cover the cedar with drywall. Can we just secure the drywall by screwing directly through the cedar into the joists? Is 1/2" drywall ok?" I'm not sure why no one responded to your post, but I could not comment on the above without further knowledge of snowloads etc. on what sounds like minimal rafters. If loads were not an issue, DW could be installed on sleepers intermediate to the rafters as a way to minimise nail pops from wood movement. Response to your second question is biased. I'm against any lighting or plumbing that involves violating the building envelope/ conditioned space.

I don't think that running the floor a different direction in the sunroom would look strange at all, especially given that you have a natural transition point in the french doors. The hardwood in my house changes direction between the living room and the rest of the house and the transition gives definition to the space. I would do the transition with a single board the width of the door jamb with the turned boards slotting into the groove in the threshold piece. I happen to like the look of a turned board underneath a door where the two rooms aren't a continuing space, such as a bathroom door. My house also has a wood floor continuing from the living room into the sunroom (no door) and over 80+ years, the house has settled slightly and there is a slight slant to one board over the transition between basement and crawl space If the subfloor construction is sufficient that direction isn't an issue, I would think the hardwood would go across the width of the room, perpendicular to the ceiling. But, that's just my opinion and worth what you paid for it!

We have given thoughtful consideration to all suggestions - thank you. I would like to ask another question - not sure of Houzz protocol about starting new thread so forgive me if I err here. We have a beautiful elk antler chandelier and thinking about where to install in the new house ... great room is obvious choice. We could hang it from the middle beam in the room - other opinions? Here is a pic. Size is approx. 42" side-to-side and it is about 28" high ... without the chain. In this picture we don't have a very high ceiling in the entry so had to squish it close to the beam.. PS To give you all an idea of our aesthetic, my husband is a bow hunter and ranch/hunting style house is naturally where we lean ...

I think your ceiling can be really beautiful. I would not drywall over it. If it were mine, I would paint out everything...the TG, beams and walls in white or off white paint colour (as already suggested) OR I would paint the TG and walls white and then wrap the beams in new wood and then stain the beams to match wood floor colour so that the beams were a feature. Whatever you decide, please show the finished reveal once you complete your project.