A1: Philips 43" 439P9H/00. Probably not recommended, as there are better models out there since it was produced. It’s great as a working station, and with proper tools (Power Toys for Windows), it smoothly becomes a display with multiple sections. That doesn’t make it compatible with full screen modes, but only for windowed programs.
A2: I don’t think it supports PIP/PBP, but I have never looked into it.