The extra parses with determiners showing up as complements
are happening because your COMPS lists are unbounded.  The
first thing is correctly constrained to be an NP, but after
that, anything goes.  Since you're using the free-word
order module, there's a rule that allows the second complement
to be realized before the first...

>I was unsure of this, because I didn't clearly understand the
>statement about English, "We have both orders (head-adj and
>adj-head), but adjectives are always prehead". I have not noticed any
>parsing behavior that seems to contraindicate this decision.

English has both premodifiers (the black cat) and postmodifiers
(the cat on the mat), but with a few exceptions (attorney general),
single-word APs serving as noun modifiers show up before the
head.

>Case is expressed morphologically with the ending -n. This ending is
>invariant.

-> _Accusative_ case is expressed...

>This test suite presupposes that inflected determiners are subject to
>the same syntactic rules as adjectives, there is at most 1 uninflected
>determiner per noun, and if present it must immediately precede the
>noun and all other premodifiers of the noun.

If the inflected determiners can iterate, it sounds like they
might not be determiners.  Do they co-occur with the uninflected
one?

>A technical error is that LKB apparently misreads the beginning of a
>test-suite file when it is encoded in UTF-8.

Does itsdb work better?  I had no problems running your test suite...
(Or maybe your itsdb testsuite is ascii?)