No, this version (USM) does not have Image Stabilization. For stabilization, you would need the 'L' series version (EF 100mm f/2.8L IS USM). A tripod is recommended for macro work.
Yes, it is a full-frame EF lens and is fully compatible with both Full-Frame (e.g., 5D Mark IV) and APS-C (e.g., 90D) Canon DSLRs.
Absolutely. The 100mm focal length provides flattering compression and the f/2.8 aperture creates a shallow depth of field, making it a favorite for headshots.