Only to clarify my thoughts in question 5.
k (break point) is a fix value for a given type of hypothesis (problem) .
k do not depend of N, it is bound to N. Correct?
Also there is 2 option for growth function:
1-if there is not a break point then

2-if there is break point

, which is polynomial of degree k
So a grow function which it is polynomial with degree variable and depending of N could not be limited by

because for big value of N the bound will not be valid.
Am I right?