Texture Clarification

Whoops!  Meant "Texture Clarification"!  Oh well...

I'm studying privately and I want to clarify some questions I have about texture so that I can make sure that I sound like I have a clue when speaking with other musicians. 

From my understanding:

• Monophonic=a single melodic line
• Homophonic=Multiple lines, all moving with (basically) the same rhythms
• Polyphonic=Two or more melodies that lay on top of one another but move independently.

I've heard some people say that Homophonic music is also polyphonic when it has good voice leading since each voice in the harmony is moving (mostly) independently in direction and interval even if not rhythmically.  Some people have said that they are different things altogether.  Which is true?

Also I've heard that in a texture when a melody is placed over a chordal accompinament it is not homophonic since all voices do not move together.  I've heard that the correct term for this is monody.  I've also heard that monody is a term for a specific style in the 17th century and that a melody with chordal accompaniment is still considered homophonic.  I've even heard that not only is it not monody and not homophonic, but is rather a less active version of polyphony.  Which is true here?

If it is true that this texture is considered monody to designate it from a completely homophonic texture.  Then, is there a term to designate other types of texture?  For example:

• Choir arrangement in which all voices move together but there is a piano accompaniment (or single voice) that moves independently of the choir although the independent line(s) is/are not the melody.
• Melody  with chordal accompaniment where the melody is not in the soprano or highest voice.
• Melody and countermelody with chordal background.  All voices in chordal background move at the same time.
• Orchestral arragement with melody and chordal accompaniment that moves in whole (or half) notes, but one or more instruments are also playing arpeggiated or repeated accompanimental patterns that repeat consistantly as to make it completely accompanimental in character rather than melodic.  (Is this accompanimental line called an obligato btw?)
• Any other alternate texture that I am not thinking of?

Thank you in advance for your assistance! :D

Your understanding of Monophonic, Homophonic, and Polyphonic is correct.  However, there could be several different interpretations that may be considered correct.  To me, Polyphonic music means "multiple sounds" or "many sounds".  Therefore, homophonic music IS polyphony because there is more than one sound.  It's one of those "a square is a rectangle, but a rectangle is not necessarily a square" kind of things.  Homophonic music is polyphonic, but polyphonic is not necessarily homophonic.

With that said, I don't think it matters.  Here's why:

Your explanations of various scenarios you outlined at the end of your post, to me, sounds much more intelligent and musically practical than any MUS101 or 202 academic jargon that Mr. FancyBear spouts out at fancy dress parties while drinking a watered down scotch.  You're asking us how you can be more clear in your speaking about musical texture.  Quite honestly, using words like Monophonic, Homophonic, and Polyphonic is more unclear than how you have already clearly stated your situations.  I know this to be true, because otherwise you wouldn't be asking us for clarity, am I right?