It's not clear what you want and/or need. And where you are makes a difference.
You, kids, an office and renter/ mom makes 2000 sq ft seem tight to me.
Will you need the home office in 10 yrs when you anticipate mom?
Re; Energy Get an energy audit once you own the home. Follow their recommendations (at least) for sealing drafts, windows, insulation, etc.
Yes, close the doors to unused rooms of the home. But also close the heating/cooling ducts and put something to stop a draft at the bottom of the door. I cut a piece of 3" Rigid-foam insulation that just fits in the heating duct and put it behind the register of my un-used room (it's actually used for storage).
Wear sweaters and slippers. Use throw rugs for cold floors.
Use fans when it's warm. I use a dehumidifier and a fan in my bedroom. On warm, muggy days I turn the dehumidifier on and close the door after dinner. By bedtime, it's quite nicer.