This is bullshit. Just created a new dummy category, then immediately deleted it and then all my issues were solved.
WHAT THE F***** . It seemed it has to do with this nleft, nright values that were regenerated for those categories.
BUG: Why does PS does not do that when you reorder categories????? Why does it only do that when creating/deleting categires?
And my other issue about attribute positions not being stored I could fix thanks to http://www.prestashop.com/forums/topic/335042-attribute-value-positioning-problem-after-16/
Sorry but this sucks, such basic things should simply work. Is this even tested before it's released???