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Signaling is the informed side taking actions to reduce (or maintain, depending on the private types) the information asymmetry. For example, high skill workers getting certifications to signal their productivity so as earn a higher wage. Or low skill workers trying to mimic the high-skilled's behavior as much as possible so that they cannot be separated.
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Utility maximization is a proposition that can neither be confirmed nor refuted. For one thing, "utility" does not even exist as an entity; it's a mere conceptual construct. For another, "maximization" as a motivation is inherently unobservable. Even behavioral economists, who are adept at finding so-called empirical "anomalies" --- behaviors that apparently ...
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No, risk neutrality is not assumed. Risk preferences are given by the concavity of $u_i$ which is arbitrary in this setup.
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There are a few imprecisions in the way you formalize things. For example saying "𝐺 is the baseline choice problem" does not make a lot of sense, because a problem should include the DM's utility, the available actions, and the belief about the state of the world. You only included the latter.
Regardless of notation, I think that you are missing the key ...
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