C3 is indeed backwards, the footprint in altium is wrong, this awkward to be the issue causing it to not oscillate.
Pin 3 goes through 1 (750ohm) resistor to Q1 base. R3 is a pull up resistor that may not be required. R1 I couldn't comment on.
The TVS is protecting just this board and attached components, which are led lights and a few accessories. The board is fed from the battery and is grounded back to the battery. I'm not sure where you have got the whole bike is protected by this one TVS from. There is also a fuse coming from that battery to this board and the rest of the bike is protected by the factory fuse box.
The bike in question is a honda crf450x enduro bike, it doesn't come with lights as standard.