Coilgun capacitor reverse voltage in my schematic?
"My question is whether the capacitor in my schematic will be able to explode due to reverse voltage or not. "


Yes it can explode when the coil current starts to decline significantly or when the reverse voltage exceeds 5% of the rated forward voltage.

You must avoid a reverse voltage being applied to the e-cap. 

The phase relationship of the RLC circuit is under your control to maximize power transfer and impedance of load.

The design could use a reverse power diode across the e-Cap. But I did not analyze the entire design for efficiency.