nominavit (SYN): what kind of a kernel does this verb represent?

A Factitive kernel with the relative pronoun quem as a direct object and Lavinium as an object complement. The gapped subject is Aeneas. ...locum, quem Lavinium nominavit.

quem (SYN): what is the syntactic function of the relative pronoun within its own clause?

It is a D.O. to the verb nominavit.

Laviniam (SYN): what is the syntactic function of this word?

IT is the Subject of the Indirect Statement governed by indigne ferret.

advenae (SYN): What is the function of advenae?

It is an apposition to Troiano (the Trojan, meaning Aeneas)

cogo (SEM): what are the two possible meanings of cogo, ere, coegi, coactus ? Which is appropriate to use here?

Collect and force. In relation to exercitus (army) collect in the sense of draft is a better choice.

progressus (SEM): note that this is a deponent verb. How will that affect your translation?

The omission of been is necessary. Having progressed, moved forward is a good translation.

Latinorum (SYN): What is the function of this word?

It is an adjectival modifier (genitive noun) to consensu. It is modified by the adjective omnium: 'with the consent of all Latins'

declaratus est (SYN): What kind of a kernel does this verb form?

Like the passive form of nomino, voco, appello, the passive of delaro represents a LINKING kernel which means that you are not baffled by the presence of a subject (victor) and a Subject complement (rex): The victor (Aeneas) has been declared a king.

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