For the separation of the unknown mixture, you are instructed to isolate the amine followed by the acid and finally the neutral.
does the order matter? if not, what other orders could be followed?

Yes, it does. The neutral must be the last because it is 'left over'. However, the order of the acid and base/amine can be switched.

Explanation:

This is commonly known as the acid/base extraction method. It involves conducting simple acid/base reactions to separate the basic, acidic, and neutral compounds present in the given mixture. The neutral compounds generally do not react chemically with either the Brønsted acidic or basic compounds. The compounds present in the mixture can easily be separated. Therefore, for the given problem, the neutral must be the last because it is 'left over'. However, the order of the acid and base/amine can be switched.