Would silver nitrate be able to tell you what halides were present in a mixture of halides?
Probably not. What might help is doing the test on known halides.
You suspect you've got an halide, on the basis of the precipitate observed with silver salt. Well, in a series of fresh test tubes, do the experiment again, but with hydrochloric, hydrobromic, and hydroiodic acids (you could do the experiment with simple bromide or iodide salts, if the acids ain't available). This way you KNOW the identity of the observed precipitates, and you can compare their colour, creamy white, yellow etc. with the precipitate you observed.
Obviously, once you've made the comparison, you have to make confirmatory tests. It has been a long time since I have done these sorts of test, but doesn't ammonia dissolve both silver bromide, and silver chloride, but fails with respect to silver iodide? Anyway, read your scheme, and plan your series of reactions.