In my default document, they are in frames 29 and 30, but no matter. I can enter the 7(b9) by typing C:29, and the 7(#9) by typing C:30. That's faster than typing out the complete suffix. Root > : (colon) > frame number.

Thanks very much Mike . Appreciate that . Yes that is a quicker way .Just wondering , as I have quite a few more  chords to try and teach Finale , do you know how the  frames are supposed to behave . I need to add  about another six or seven new suffixes to the set I have so far taught Finale . I don't want to waste my time , only to find Finale works in a different way to how I am imagining . It seems as tho I will have to teach Finale each new suffix  for each and every note  i.e. built on C , Db, D ,Eb etc etc .     - I don't seem to find a way to get Finale to recognize the relative relationship between the same group of notes  , and simply apply that suffix  to whatever root note I apply  .     

You shouldn’t have to do that. Once a suffix is stored, you can apply it to any root, either by entering it directly, or with the colon. 

Do the suffixes you’ve “taught” appear in the chord frames?

So , I should be able to play the chord on my kbd , and so long as I have taught the chord to Finale , and there is a suffix stored in one of those boxes / frames , Finale should display it for all the degrees of any scale ...

Yes by the way , the suffixes do appear in the chord frames

No Sorry about this ,  but there must be something going wrong here ,  As  , now Finale is no longer displaying the C9 which I taught it hours ago ,  for some weird reason it is now displaying it as C7(b9) .. 

To further explain ,  I wish to arrive at a situation where I can play the exact chords on my midi kbd , and have them be inputted correctly for the main bulk of chord symbols .  - That would be C, Cm, C6,  C7,  C∆,  Cm7,  C9,  C11, Cm9,  Cm11, C69, Co, Cø, Cm6  C∆(#11)  C7(#11)  C7(b9), C7(#9) C7#5    .     After these ,  I intend to use the colon and select the relevant suffix ID for the others .

I have been working on this for days , and am hoping that it is achievable within Finale , but I am beginning to think Finale isn't capable of working in this manner due to the number of instances where Finale displays the wrong chord suffix . 

IMO, it's more efficient to simply enter the suffix ID manually. The fact that you've spent days on this method should tell you that your time is more valuable than spending it trying to teach FInale.

… now Finale is no longer displaying the C9 which I taught it hours ago …

This is a misunderstanding.

Chord symbols are document specific, not program specific.

Finale stores Learned Chords along with regular Chord Suffixes in a Chord Suffix Library.

Therefore, you can load the Learned Chords you create in one document, into another document without having to redefine the Learned Chords.

Also, Learned Chords are key specific.

Example:

C9 as a {Learned Chord in the key of C major} is not a {Learned Chord of C9 in the key of F major}.

C9 as a Learned Chord in the key of C major = F9 as a Learned Chord in the key of F major.

In Other Words:

The chords you taught Finale “hours ago” in another document, are not Learned Chords in the document you are working on now (which, perhaps, is not in the same key as the first document).