Do we know the formula for ilford Ilfotec DD-X?

or does anyone have ideas, thoughts, or "a hunch" speculation. . . . . etc. on what is in DD-X?

is this a fine grain developer or high acutance? or maybe something in between ?

No need for speculation. From The Film Development Cookbook:

DD-X is a conventional PQ/Boraxdeveloper with a moderate pH around 8.7. DD-X employs a high amount of potassium sulfite to aid concentratability. What makes DD-X unique is that while concentrated developers typically employ carbonate or hydroxide as alkali, DD-X uses a gentle borax-boric acide buffer.... DD-X is a concentrated ID-68 or Microphen, the main difference being the use of potassium rather than sodium sulfite... From the foregoing it should be clear that DD-X is a solvent developer.

Thank you , Alex … cheers

I should also note that TFDC recommends DD-X for moderate to extreme pushing and attempts to explain (or understand) why (chapter 10).