What form of "to be" to use with "former/latter"?
'Former' and 'latter' are ordinal adjectives, not nouns. (The same is true of 'First', 'Last', etc.) The morpheme[s] for quantity are to be found on quantifiers and nouns, not adjectives. 'Former' and 'latter' are pointers to 'parallel' antecedents, which must be 'universities' and 'polytechnics' (the only list in the first sentence), and each of those nouns is plural, so the verb 'are' is used for agreement.