YOu can only solve 10 & 11 after you have all your tech. 12 you can already do now. It requires 1 tech maxed and a 'master'
I don't remember 9 off hand so I can't givce you a hint there.
As to where 63 is enough. it depends. Once you have all your tech, there is a 'chance' of solving a puzzle with each birth. I usually get it quickly but other people have reported it taking longer.