I have acetylne and electric welding equipment. I weld for fun not professional at all, but have these 2 comments on the above:
I'm surprised that electric welding will blow your lights as the voltage is so low and the bulbs are not in the circuit but if it's happened to you then obviously it can happen... Maybe it's in the arc... (or are you sure the trailer didn't get hit by lightening just after you had it welded!
And as for wheel locks, I can't say I've tried but I'd be surprised if my acetylne torches could not cut them off as I've never hit anything I haven't been able to cut with the cutting head on it... but y'never know till you try...