You have been refering to the Ferroxcube handbook in a previous post. I think, that most of your question can be answered
from a thorough literature of this or other manufacturers publications, at least generally.
There are also profound text books, e.g. Snelling, Soft Ferrites. You can try to locate at a good engineering college library
or as E-book on the internet.
Some answers from my side:
1) They are manufacturer specific. You should be able to find a cross reference by comparing some corner data.
2) Answered in detail in the Ferroxcube handbook, see chapter Literature and reference publications
3-8) Depends on which of the inductive component's parameters are significant for your circuit. In my opinion, the question
isn't specific to ferrites, it's rather a general circuit design question, like "what's the importance of resistor power rating".
Or ask a baker, how to choose the best flour for his bread... You can easily write complete papers or even books about it.
9) Depends on. Sine for signal, square wave for power applications. Frequency ranges are never sharp for ferrites, so
the difference probably doesn't matter that much. If e.g. core loss is the question of interest, the fundamental would make
the largest part anyway.
10) Ferrites itself have no low frequency limit. A transformer has a low frequency limit either set by saturation flux or L/R time constant.
11) I assume, that the discussion is restricted to soft ferrites. They are mostly used as linear components, also in switching
applications. The optimal core parameters are however partly different for different applications. You'll be aware of,
when either browsing the datasheets or calculating a core for a particular application.
There are however some distinct non-linear applications of soft ferrites, e.g. transductors or special shaped cores, that
achieve a partly saturations. Or fluxgate magnetometers.