How is the purity of a compound determined?

Why is the test for nitrogen,sulphur,or halogens not carried out by the direct addition of reagents to an organic compound?

Three students,Manish,Ramesh,and Rajni were determining the extra elements present in an organic compound given by their teacher. They prepared the Lassaigne's extract $(L.E.)$ independently by the fusion of the compound with sodium metal. Then they added solid $FeSO_4$ and dilute sulphuric acid to a part of the Lassaigne's extract. Manish and Rajni obtained prussian blue colour,but Ramesh got red colour.
Ramesh repeated the test with the same Lassaigne's extract,but again got red colour only. They were surprised and went to their teacher and told him about their observation. Teacher asked them to think over the reason for this. Can you help them by giving the reason for this observation? Also,write the chemical equations to explain the formation of compounds of different colours.

Why is nitric acid $(HNO_3)$ added to sodium extract before adding silver nitrate $(AgNO_3)$ for testing halogens?

When sodium fusion extract of an organic compound is boiled with iron$(II)$ sulphate solution followed by addition of concentrated $H_2SO_4$,it gives a Prussian blue colour. This confirms the presence of which element?

Match Column $-I$ with Column $-II$.

Column $-I$	Column $-II$
$(A).$ Dumas method	$(3).$ Nitrogen gas
$(B).$ Kjeldahl's method	$(5).$ Ammonium sulphate
$(C).$ Carius method	$(1).$ $AgNO_3$
$(D).$ Chromatography	$(2).$ Silica gel
$(E).$ Homolytic fission	$(4).$ Free radical