Actually, it seems that the most common modern point of view is that most Italian plurals come from the accusative plural, after the regular transformation that turned final /s/ into /j/. This explains perfectly also the third declension (so the ending -es became -ej>i). For example, from Martin Maiden's A linguistic history of Italian, section 2.12
An alternative [to the derivation of plurals from nominative], and in our view more plausible, approach is to view inflectional -e and -i as phonetic developments of the unstressed vowels, triggered by original final [s]. Inflectional -s survives intact in Ibero-Romance, Gallo-Romance and Sardinian. Traces of inflectional -s also appear in some northern Italian dialects. After a stressed vowel, [s] has generally become [i] in Italo-Romance: noi ‘we’ < NOS; voi ‘you’ < UOS; poi ‘then’ < POS(T); crai ‘tomorrow’ < CRAS (in southern dialects); stai ‘you stand’ < STAS. This lends weight to the view, proposed, for example, by Reichenkron (1939) and Lausberg (1965: 431–3), that unstressed final [as] and [es] yielded *[ai] and *[ei] (Lausberg actually proposes *[ai] and *[ei]), which subsequently monophthongized, to [e] and [i].
[...]
The facts are strongly consistent with the hypothesis that inflectional -e and -i do not directly continue Latin inflections containing front vowels. There is no palatalization whatsoever of velar consonants before the feminine plural inflection (nor before the second person singular indicative inflection -e of the OTuscan first conjugation): e.g., aˈmiːka ‘friend’, aˈmiːke; ˈgrɛːka ‘Greek’, ˈgrɛːke; ˈfiːzika ‘physical’, ˈfiːzike; ˈlarga ‘broad’, ˈlarge; ˈbjaŋka ‘white’, ˈbjaŋke. This absence of alternation in the feminine is repeated throughout the modern Italo-Romance dialects.
To address your other point, some kind of intervocalic voicing of consonants happened, most notably in Northern Italy, but really across the whole peninsula: for example see strada (from stratam), lago (from lacum), riva (from ripam), etc. so cittade is not really that much of an outlier (but cfr. with virtute). Maiden, in section 2.7, says about intervocalic voicing:
Voicing of intervocalic short voiceless consonants is a characteristic of northern Italian dialects. [...] That some instances of intervocalic voicing in Tuscan may be attributable to borrowing from northern Italian dialects of words containing voiced consonants is entirely plausible. [...]
A number of words showing intervocalic voicing are so rooted, semantically, in the ground of everyday life that an exotic origin is implausible. [...] A further argument against the hypothesis of a northern origin for consonant voicing is the striking absence of words displaying that shortening of long consonants (see section 8) which characterizes all northern dialects, and which some scholars group with northern Italian voicing under the general label of ‘lenition’. [...] So the problem of intervocalic voicing remains unsolved.
