Damn, I can't imagine how you felt...
Only the unique experiences in this thread are enough to know how f*cked up AWS billing is.
¯\_(ツ)_/¯
Reading the docs I got the feeling that the product is designed for big cooperations only. But not for someone who wants real price control. The free account just made no sense to me.
I ended up renting a cloud server ~3€ a month. (Not AWS) Looking at this thread this was the best decision I could make.