Proteins have primary structure. If you are given a method to know which amino acid is at either of the two termini (ends) of a protein, can you connect this information to purity or homogeneity of a protein?

Yes, if we are given a method to know the sequence of proteins, we can use this information to determine purity of a protein. It is known that an accurate sequence of a certain amino acid is very important for the functioning of a protein. If there is any change in the sequence, it would alter its structure, thereby altering the function. So by knowing sequence of a given protien, we can determine its structure and compare it with any of the known correct protein sequence. Any change in the sequence can be linked to the purity or homogeneity of a protein.

For example, a single change in the sequence of haemoglobin in P chain at 6th position can alter the normal haemoglobin structure to an abnormal structure that can cause sickle cell anaemia.