Agree with all of the above. Somehow (even if a robot), you seem to have gotten the wheel built at 4:30 on Friday afternoon by the guy they hired on "Hire a Dummy" day.
To keep weight down, a bike wheel is a bit of an engineering marvel. You are 1000% correct that all these broken spokes early on point to bigger problems in the wheel.
At this point, the wheel needs professional help. The only questions are who does the work and how much you end up out of pocket.