Learn German: Die Situation ist völlig eskaliert am späten Nachmittag. - The situation escalated completely in the late afternoon.

In strict standard German word order, the past participle eskaliert would go at the very end. However, placing a prepositional phrase after the final verb (into the so-called Nachfeld or after-field) is very common in everyday German. It is often done to add an afterthought, to emphasize that specific piece of information, or simply to prevent the middle of the sentence from becoming too clustered.

Why do we use ist instead of hat for the perfect tense of eskalieren?

We use the helping verb sein (here conjugated as ist) because eskalieren is an intransitive verb that describes a change of state. The situation changed from stable to chaotic. Verbs that describe a change of state and do not take a direct object always use sein in the perfect tenses.

Why does the adjective spät get the ending -en in am späten Nachmittag?

This is a good refresher on adjective endings. The preposition an merges with the dative masculine article dem to form am. Because the article is already doing the heavy lifting by clearly showing us the case and gender (masculine dative), the adjective that follows it takes the weak ending -en.

Could I use ganz instead of völlig to mean 'completely' here?