I can answer a few of these questions, from the point of view of someone who knows a good deal about the languages that inspired Eddy.
With free word order, what happens when the subject and object share the same class, number and person - how can a listener tell which is the subject and which the object?
This is the beauty--one might even the say the raision d'etre--for the 4th (obviative) person. In the Algonquian languages, which are head-marking in the way Eddy's is, there can never be two third persons in an expression: one will always be obviative, usually the object. Thus, you will never have 3rd-person + third-person sentences. And reflexives are done, at least in the natlangs, by using a reflexive marker and detransitivizing the verb root. (I've mentioned before that the obviative tends to be pooly understood; here is the major reason it came about, and why it exists, and the context in which it makes sense.)
Noun incorporation strikes me as a bit vague - what does the speaker imply when a noun gets incorporated (or is it just a whim)? When does incorporation happen, when can it not happen? Is there a preference for objects to be incorporated, or subjects? etc
Incorporation can serve a semantic or purly aesthetic function. E.g., Mohawk speakers consider it inelegant to use free-standing nominals when they can be incorporated; you can also "background" a nominal by incorporating it. The rules of various languages vary on what can and cannot be incorporated; Mohawk allows many objects to be incorporated, but also allows subjects to be incorporated in certain kinds of intransitive expressions.
Why can locational morphemes only be used with incorporated nouns? What happens if the sentence doesn't include the noun?
This, I think, is Noyatukah influence on Eddy. In my language, all non-subject and non-object nominals are always incorporated; and so locatives only ever appear attached to incorporated nominals. The reason is largely that non-subjects and non-objects are never direct participants in an action; they are always, to one degree or another, background information.