from wikipedia
A)All models support software emulation of the original PlayStation,[68][69] but support for PlayStation 2 backward compatibility has slightly diminished with later compatible models and the last model to have integrated backward compatibility was the NTSC 80GB (CECHE) Metal Gear Solid 4 Bundle.[70] Compatibility issues with games for both systems are detailed in a public database hosted by the manufacturer
B)being how most 3rd party controllers lack sixaxis, games that have sixaxis won't recognize them so you might just want to get an official controller
III) Infamous 2, Ninja gaiden Sigma, Ninja Gaiden Sigma 2 No More Heroes: Heroes's Paradise, Sly Cooper: Theives in time, Tales of Graces f, Tales of Xillia, Valkyria Chronicles