As you say, either word can be appropriate, and they express two different things:
He gives examples to illustrate his life with friends in the past and [to] express his feelings about his life now.
He gives examples to illustrate his life with friends in the past and [he] expresses his feelings about his life now.
The rule that clarifies the meaning is simply the form that the verb takes. However, as Colin has pointed out in the comments, similar sentences may be ambiguous. For example:
I give examples to illustrate my life with friends in the past and express my feelings about my life now.
In this sentence, "[to] express" and "[I] express" are indistinguishable. Grammatically, this sentence is ambiguous. However, the probable meaning can be understood from context. The phrases "...illustrate my life with friends in the past..." and "...express my feelings about my life now..." have an obvious parallel structure, so most native speakers would assume the "[to] express" meaning.
The ambiguity of the new example can only be resolved with complete certainty by changing the structure of the sentence, such as by including "to" or "I".