I would like to divide a room into two rooms with a dividing wall. Should I remove a portion of the ceiling drywall, and drywall on abutting walls, and should I remove the portion of the subfloor to attach the new partition framing directly to joists, studs and floor joists?
You're asking a simple question and I'll provide a simple answer but in order to meet building codes this may get a little complicated for you.
Yes- You will need to remove drywall and attach the framing of the new wall to the existing framing. There shouldn't be a need to cut through the subfloor. The baseplate or footer of the framed wall can attach directly to the subfloor.
However, beyond that it gets more complex. You will need to get a permit and check your local codes. Constructing a separate room will need to meet codes regarding ingress and egress, electrical (light switches, outlets) and possibly other requirements such as a closet if you want it to be classified as a bedroom. You will also need to think about heating and cooling which may require adding ductwork or baseboards. In other words it's not as simple as just building a wall.
No. Many a partition wall has been installed right over the existing drywall. I've done so many times myself when remodeling homes for myself and others.
If you're able to attach the wall top and bottom it's not going to be a problem. Some construction adhesive behind the stud against the old drywall will prevent cracks in the new tape joint.
Fasten your new wall in as many points of indirect contact with framing as you can. Give it the thump test to see if it feels solid. Unless you have some extraordinary loads planned for it there won't be an issue.