Is it possible for a fighter jet to shoot itself down with an IR missile?
Not really, it would take any of these missiles so long to turn 235 degrees (way more than 6-10 secs), which is generally the maximum burn time of most of their rocket engines. Plus, if it did somehow, get turned around 235 degrees, the energy (airspeed) bleed from such a large turn would leave it without any energy to intercept the launch aircraft even if by some miracle it acquired an IR lock