Doctor with ultherapy machine: will this procedure also smooth out fine wrinkles around my eyes and on the forehead (this way no botox each 3 mos)?

NO. Ultherapy machines use focused energy of ultrasound to heat deeper structures. The problem is like with many other devices, that this energy is not delivered and absorbed evenly and the long term results are far from good. With eventual destruction of fat under the skin and hollowing of the face as a result.
Be careful! I would be surprised if this doctor with the ulthera device said it would smooth out wrinkles like botox. There are other devices that use rf energy (in clinical trials) that may help with this but ulthera was not designed for this.