No it should not be fed in their water.
You need to direct dose each bird straight to the beak no less than twice a day with it. Three times is better.
Dose here:
https://www.backyardchickens.com/threads/treating-and-preventing-diseases-with-tylan-200.1241683/#post-19926142
Your state lab is listed here.
NECROPSY & DISEASE TESTING LABS
You can have testing done, usually just a swab taken by you and sent (mailed) in, to know what your are dealing with.
Almost all chicken diseases are spread extremely easy so if one in your flock shows symptoms then it is extremely likely they all have it/have been exposed and are carriers already.