Re: Yon/Shi and Nana/Shichi
I looked at the compounds listed under SHI in the revised Nelson dictionary. (They are listed on pp. 238-240.) It is very hard to find any rule that determines when to use SHI or when to use yon. I suspect that the determining factor is usage, probably influenced by concepts of euphony (i.e., what 'sounds' right to a native speaker).
Thus, I have never come across shi-kyu or shi-dan, but equally, have never come across yon-hou (4 directions), yon-gatsu (April), or yon-ki (4 seasons, especially the work by Vivaldi, which is very popular here). There are 149 homophones of SHI listed in the Nelson dictionary, by the way (and by "homophone" here, I mean different Chinese characters for the same sound 'shi').
The situation with SHICHI is somewhat different. There is only one homophone (SHICHI = hostage, also read as SHITSU = substance). However, there is no rule beyond that determines whether it is SHICHI or nana.