Rotted Sill Plate and Joists
1. Do I need to completely remove the sill plate if it is such a small section? The section that is rotted is where the jack and king stud connect to the sill plate. = Yes, or the window could break when the supporting stud and trimmer fail and settle. (at any time)
2. Should I use some of the composite material to build up the 2x4 = No, use a pressure treated 2x4 plate with anchor bolts drilled into the slab.
3. Should I cut the small section out? = Yes, as above with sill sealer under, or caulking- 3 beads.
There should be a house wrap or builder's tar paper over the exterior wall board to stop moisture from soaking said material. There should be weep holes in the brick veneer wall at the bottom, every few feet to drain any condensation. Caulk the shutters' attachment bolt holes. Make sure there is metal flashing under the bottom siding piece onto the brick. Lift the flashing's edge on the brick, run a bead of caulking there.
The rot is the end result of the fungus growing there. Google- "dry rot" or "fungus". You may need to spray with water and a 10% bleach solution to stop it.
Be safe, G