hi, i have scanned for you extracts of some books i have on these questions:
(a) iota in long diphthongs: the iota was pronounced during the classical period, influencing some (but not all) Latin loanwords. see the following scans of Allen 1987 (Vox graeca) and Threatte 1980 (The Grammar of Greek Inscriptions) which discuss this (remove spaces):
www . freewebs . com / mhninaeide / Allen1987andThreatte1980 . pdf
see in particular pg 86 of Allen on Latin loanwords.
(b) lunate sigma: this was the common written form in the classical period. see the following scan of the papyrus alphabets (literary and cursive) from Thompson (An Introduction to Greek and Latin Palaeography):
www . freewebs . com / mhninaeide / Thompson . pdf