Question 2: PS is a brittle polymer, that's why users generally prefer copolymers like ABS and SAN. ABS offers much plastic deformation before it breaks. I didn't try SAN. You could check some datasheets for SAN and ABS, especially the "elongation at break", possibly the tensile strength too, to draw curves that compare this behaviour.
Question 3: the general idea is that stress alone doesn't make the plastic deformation. Heat provides the energy, and when by chance much energy is concentrated at one place, stress can break some bonds, often intermolecular ones. The hotter, the more often this happens. So the frequency of the oscillating deformation where losses are highest increases with the temperature. Keyword viscoelastic behaviour, it's often measured in torsion.
While I've already seen such temperature-frequency curves, or even temperature-frequency-losses curves, I didn't know there were some analytical relation with Tg, the glass transition temperature.