By definition STOPWAY starts where TORA ends but can it be used for the TORA of the opposite runway (Can stopway be used for "initiating the take off run").
Other than perhaps specific situations, the general answer is no, one cannot use a stopway to initiate a takeoff from the opposite runway. A stopway doesn't become a "displaced threshold" for the opposite runway.
Generally:
1) A stopway by definition isn't part of the runway (it's an area "beyond the takeoff runway")
2) A stopway might not be constructed to the full strength of the runway
3) There may be other restrictions (e.g. blast areas) preventing use of the stopway as a takeoff surface
4) Taxiways don't serve / extend into stopways
Stopway is always available as clearway up to the clearway limit.
I may be misunderstanding the above, but from my interpretation... no a stopway isn't always available as clearway. In particular, a clearway must be
at least 500 ft wide, while a stopway may just be the same width of the runway.
(Clearway - Stopway) could be positive, zero, or negative.