In italiano "attività" è invariabile, however in English I think both forms "activity" and "activities" are correct.
Indeed "La città era piena di attività" means that there are many activities.
Perhaps, but in English 'full of activity' is a much more common phrase; one rarely says a large place is 'full of activities'.
That's what i put too. I think the elision (contraction of the di) does not occur if the noun is plural.
Here is the explanation I Googled (provided by Necsus on the Word Reference forum) : "It is normal to have it with singular articles and respective prepositions combined with an article (l'uomo, dell'altro, un'amica), with singular demonstrative adjectives questo, questa, quello, quella (quest'uomo, quell'amica), with bello, bella (bell'uomo, bell'amica), with santo, santa (Sant'Antonio, Sant'Anna), with di in d'accordo, d'epoca, d'oro (but optional before a verb: d'essere o di essere), with come and ci before the verb essere (com'è successo, c'è) and with some idioms: a quattr'occhi, l'altr'anno, tutt'altro, senz'altro, nient'altro, nessun'altra, tutt'al più, mezz'ora, buon'anima, quand'anche. In other cases the elision is always optional, it occurs especially with the monosyllables, particularly with the preposition di, and it is more frequent when the initial vowel of the following word it is the same and it is unaccented (mi importa => m'importa), or when they follow another monosyllable with same vowel (lo ho detto => l'ho detto). It's not possible to elide the preposition da, except in the expressions d'ora in poi, d'ora in avanti, d'altronde, d'altra parte. "
"Plenty" would have to be used with "to have" i.e. "it HAD plenty of activities" whereas in this sentence they're using "to be" i.e. "it WAS full of activity". You couldn't say "it was plenty of activities". If you said "There were plenty of activities in the city" it would be correct English but quite a different sentence from the original one given.