Not required to post anything, doesn't likely require neighborhood review unless it's a zoning variance or CHAP district, and may not be required to have plans per se but they need a building permit. You can check the existing permits site and see if they have a permit; if they don't you can file a 311 for unpermitted work and get an inspection on the property. This ensures work is done to code, safely for neighboring propeties, and that it's reflected in the tax assessments.

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In my neighborhood (Canton), third floor additions that are under 35 feet overall and set back from the front facade do not go through special zoning hearings. It wasn’t always this way—when I first moved here you saw zoning notices for hearings on these, but they are not required now.

No. It just looks stupid.