Would the broken Black Widows disclose the Jewels they wore? Quite possibly. Feel free to have Takame ask in the question thread. Any context you'd like to provide around how he asks (if he's brusque and upfront or if he dances around the topic with polite small talk at first, etc) is welcome.
Is there a way to detect Jeweled strength before someone was broken? Yes. As far as the Blood are concerned, the mind is a literal web that stretches in the abyss at the level of one's Jewel. When someone wears Birthright Summer-sky, that mind-web (for lack of a better term) exists within the range of a Summer-sky Jewel within the abyss. When you make your Offering, that web shifts deeper into the abyss. Again, this is quite literal. People can dip into someone's mind and reach that web, provided they wear a darker Jewel. You can do this politely with permission (which Fayura has mentioned in passing to Haein and/or Jon, if we recall correctly), or you can do this violently without permission (this latter is one of the ways the Blood can be broken).
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Is there a way to detect Jeweled strength before someone was broken? Yes. As far as the Blood are concerned, the mind is a literal web that stretches in the abyss at the level of one's Jewel. When someone wears Birthright Summer-sky, that mind-web (for lack of a better term) exists within the range of a Summer-sky Jewel within the abyss. When you make your Offering, that web shifts deeper into the abyss. Again, this is quite literal. People can dip into someone's mind and reach that web, provided they wear a darker Jewel. You can do this politely with permission (which Fayura has mentioned in passing to Haein and/or Jon, if we recall correctly), or you can do this violently without permission (this latter is one of the ways the Blood can be broken).