the phrase Alice Smith and my sister are in apposition, with the appositive...

[GoldfishLord]

For example, in the two sentences below, the phrases Alice Smith and my sister are in apposition, with the appositive identified with italics:
(Reference: https://en.m.wikipedia.org/wiki/Apposition )
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Q1: I'd like to know if "the appositive identified" is a shortened form of "the appositive that is identified".
Q2: I'd like to know what "with" means in that context.
Q3: I'd like to know if the use of "identified" exactly matches definition 1 at https://learnersdictionary.com/definition/identify

 

[GoesStation]

Q1: I'd like to know if "the appositive identified" is a shortened form of "the appositive that is identified".

No.

Q2: I'd like to know what "with" means in that context.

The last part of the sentence could be rewritten … the phrases "Alice Smith" and "my sister" are in apposition; the appositive is identified with italics.

Does that help? I won't address the dictionary question. I don't think it's helpful.