1. They never said exactly what transpired, only the aftermath. Bao-dur was the nutty idiot who activated it.
2. It was stated they were elsewhere battling a different contingent of Mandalorians. However, one of the load screen texts on Malachor said Revan used Trayus Academy to guide the battle against Mandalorians, but it didn't say that Revan was at the actual facility though.
3. Malak probably knew of Trayus Academy, but to what extent he may have utilized it is unknown. However, the academy near Dreshdae on Korriban was probably more active, not to mention Malak was fixated on the Star Forge.
4. Hard to say. It had been suggested that Nihilus roamed the fringes of the galaxy like a nomad. As for Sion, he may have remained on Malachor during Malak's reign.
5. It was a Republic ship, since Mandalore/Canderous identified it as one of the ships present at Malachor 5. Since Revan & Malak didn't get to the Star Forge until after that battle, the ship Nihilus salvaged was not Rakatan.